Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How do gravitons and photons interact? First of all, I am a noob in physics (I‘m a computer scientist) and started reading Hawking‘s „A brief history of time“. In Chapter 6 he says that “electromagnetic force [...] interacts with electrically charged particles like electrons and quarks, but not with uncharged particles... | Gravitational lensing (light being "bent" by stars for instance) relates to general relativity, the graviton is a theorised particle in quantum field theory. There is currently no complete and accepted theory of quantum gravity which connects the two.
In general relativity the curvature of spacetime alters the path of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/549411",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Where does the energy of a spinning diver go? Ok, before we get to my question, I will describe the problem. You have a diver who jumps off a bridge with a slight angular speed about his center of mass (figure 1). While in the air, he curls into a ball. Only gravity acts on the person while he is jumping, and since gra... | You already have your answer:
But, it takes energy to curl up and un-curl.
Your muscles do work to move your body. That is where the "chemical energy" you are asking about goes.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/549524",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Can a very small piece of material be superconducting? The existing theory of superconducting seems to be based on statistical mechanics.
Can an ultrasmall piece of material, like a quantum dot with very few atoms (like a small molecule), be superconducting?
For example, can a cubic of 3 * 3 * 3 = 27 copper atoms be su... | First you need to define what "being superconducting" means for a finite-size (small) system.
From a theoretical point of view, superconductivity (as many other broken-symmetry phases) is defined in terms of long-range order, that is some correlation function $<\rho(r)\rho(0)>$ stays finite as $r$ goes to infinity. The... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/550244",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
Why is the Force of Gravitational Attraction between two “Extended” bodies proportional to the product of their masses? Newton’s Law of gravitation states that force of attraction between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between them.... | If to be summarized in short - you need to apply and solve second Newton law equation for two-body problem :
$$ \vec F_G = \mu \, \vec r^{\,\prime \prime} $$
Where $\mu$ is two-body system reduced mass :
$$
\mu ={\cfrac {m_{1}m_{2}}{m_{1}+m_{2}}}
$$
Btw, it's interesting to note that reduced mass has reciprocal additi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/550387",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 9,
"answer_id": 5
} |
Actual meaning of refraction of light The definition of refraction which I found on wikipedia is
In physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium.
But in the below case, there is no change in direction of light. So, is this also ref... | Actually refraction is the phenomenon in which speed of light changes when it passes from one medium to another. The change in direction can be explained by Fermat's principle which you can check on Wikipedia.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/550515",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Does bending your arm in space require any energy? Since your are weightless in space, your arm has no weight, right? Does this mean that bending it in space requires no energy? Why or why not?
| The short answer is yes, bending your arm in the weightlessness of space still requires energy. You are correct that bending your arm does not require us to overcome the weight of your arm, but we do have to overcome its inertia. Inertia refers to the sluggishness that massive objects have (even in the weightlessness... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/550771",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 6,
"answer_id": 0
} |
Doppler effect of light when it's windy I think I understand the classical doppler effect in sound, where the equation is non-symmetric whether the source of the observer is moving because the speed of medium where sound wave propagates is different according to each of the observers.
I think I also understand why dopp... |
I have to somehow take in to effect the slowdown of light, the lenght contraction of space as well as the fact that for 2 observers, the light is now travelling at different speeds.
It is considerably easier than that. You simply use the relativistic velocity addition formula adding the speed of the medium in the fra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/550828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Should the thermos flask better be half full or half empty? Every evening I am preparing hot water for my two year old son wakes up in the night to get his milk. We use a rather bad isolation can for this. It is a typical metal cylinder shaped can holding half a liter. If I put cooking hot water into it, I know that ab... | The idealised formula (lumped thermal analysis) for a cooling object, according to Newton's Cooling Law is:
$$T(t)=T_{\infty}-(T_{\infty}-T_0)\exp\Big(-\frac{t}{\tau}\Big)$$
where $\tau$ is the characteristic time:
$$\frac{1}{\tau}=\frac{U A}{m c_p}$$
with:
*
*$T(t)$ is the temperature of the object in time $t$
*$T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551001",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Is the average force calculated from $F(x)$ the same as that calculated from $F(t)$? Say a force is doing work on an object in one dimension. I could calculate the average force over the distance with
$$\frac{1}{\Delta{x}}\int_{x_1}^{x_2} F(x) \text dx$$
If I also formulated force as a function of $t$, I could calculat... | To show constructively that these quantities are not equal in general, let's consider an object undergoing simple harmonic motion over a quarter-cycle (i.e., from the equilibrium position to maximum displacement.) In this case, we have
$$
F(x) = - k x, \qquad x(t) = A \sin \omega t, \qquad t \in [0, \pi/(2\omega)],
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 5,
"answer_id": 4
} |
Expression and explanation of quantum mechanical harmonic oscillator I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Quantum Mechanical Harmonic Oscillator, the author says the following:
Fig. 2.6 shows the vibrational levels in a PE [potential ... | If we have a Harmonic oscillator with Hamiltonian
$$\hat{H}=\frac{\hat{p}^2}{2m} + \frac{m\omega^2x^2}{2},$$
then, by solving the Schrödinger equation, we obtain its energy states as
$$E_n = \hbar\omega(n+\frac{1}{2}), n = 0, 1, 2,...$$
We could remove $\frac{1}{2}$ by shifting the energy origin (and sometimes it is do... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551642",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
A uniformly polarized sphere Say there is a polarized sphere with polarization density $\vec{P} = \alpha \hat{r}$. How can I tell if the electric field outside of the sphere will also be radial? I see in many places that it is taken as obvious, but why is it?
*Edit: rephrase
| Pay attention to the fact that the sphere you are considering is not uniformely polarized: only the magnitude of the polarization density is uniform, while its direction changes at each point. In particular the direction of $\vec{P}$ is radial. Therefore the system has a symmetry with respect to the center of the spher... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551770",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Equation of motion for a particle under a potential in special relativity The equation of motion of a particle in Newtonian mechanics in 3D under an arbitrary potential $U$, is written as $$m\frac{\mathrm{d}^2 \mathbf{r}}{\mathrm{d} t^2}=-\nabla U.$$ Now, my question is, how can this be generalised to Special relativit... | In this context, the question that I posted yesterday seems to be relevant. That is,
Is there anything like relativistic potential energy? If not, why? We know relativistic force along the direction of velocity, involving γ3. We also have the standard expression relating force and potential energy in Newtonian mechanic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551866",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
What does CERN do with its electrons? So to get a proton beam for the LHC, CERN prob has to make a plasma and siphon off the moving protons with a magnet. Are the electrons stored somewhere? How? I don’t mean to sound stupid but when they turn off the LHC, all those protons are going to be looking for their electrons. ... | Just to add an electrical engineering answer to these good physics answers, insulators are never perfect. In school we talk about perfect insulators, but in practice everything has some level of conductivity. Air itself has a resistivity of somewhere on the order of $10^{16}\Omega-m$, for example.
Usually when doing ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/551992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "35",
"answer_count": 5,
"answer_id": 1
} |
What does it mean to say the CMBR has a “temperature”? We say the cosmic microwave background radiation “has a temperature” of 2.7K.
Does this mean it has a temperature in the way we say the air around a warm lightbulb has a temperature of 120° or in the sense that the mix of electromagnetic waves given off by the ligh... | It means the mix of electromagnetic waves "given off" by the CMB (really: "that constitute the CMB") are like those emitted by a blackbody at 2.7K.
Temperature is a property of an ensemble of particles (photons in this case, could be air molecules, or even virtual particles) but not of space itself.
Yes, people speak ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/552190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Angular momentum of the earth We know the tidal waves are decreasing the spin rate of the earth which causes the days to longer, so as the angular momentum of the earth decreases it means it rotational kinetic energy also decreases since energy is always conserved the translational kinetic energy of earth must increase... |
since energy is always conserved the translational kinetic energy of earth must increase now right?
Energy is conserved, but kinetic energy is not necessarily conserved. In this case, the tidal drag converts some of the kinetic energy of the earth-moon system into thermal energy.
It's very similar to simple fricti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/552355",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
What happens to an inductor if the stored energy does not find a path to discharge? Suppose an inductor is connected to a source and then the source is disconnected. The inductor will have energy stored in the form of magnetic field. But there is no way/path to ground to discharge this energy? What will happen to the s... | The current will flow back and forth between the end points of the wire after the potential difference is removed. It is like a wave traveling back and forth on a string. This is because all of the electrons are behaving as one wave (wave function) in the superconducting regime. If there is no heat loss this will cont.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/552611",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 10,
"answer_id": 7
} |
Why is (anti)-holomorphicity considered in physics? As a mathematician, holomorphicity is an extremely good property that provides rigidity, finite dimensionality, algebraicity. etc to whatever theory that's considered. I'm curious about why (anti-)holomorphicity is considered in physics.
As an example, apparently hol... | Scale invariance is common in physical systems at phase transitions. If the characteristic length of a system is small in one phase (disordered) and infinite in another phase (ordered), then typically the system is scale invariant at the transition between the two phases. A non-trivial physical observation is that in m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/552772",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Derivation of Lorentz transformation I am reading Lorentz transformation from Robert Resnick book. It is given that
$x'= a_{11}x + a_{12}y + a_{13}z +a_{14}t$
$y'= a_{21}x + a_{22}y + a_{23}z +a_{24}t$
$z'= a_{31}x + a_{32}y + a_{33}z +a_{34}t$
$t'= a_{41}x + a_{42}y + a_{43}z +a_{44}t$
While solving coefficients of ... | You can think of Lorentz transformation similar to a rotation in $x$ and $t$ plane ( if the velocity is along x axis) , so basically its just intermixing time and only $x$ component of space. So $a_{42} $ and $a_{43} $ will be zero as there is no velocity along $y$ and $z$ axis.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/552992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why do we need a lens in the delayed-choice quantum-eraser experiment of Kim? This is the delayed-choice quantum-eraser experiment of Kim diagram described on Wikipedia https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser
Why do I need a lens in front of the D0? Why we should focus photons? The classic Double-s... | From the paper Taming the Delayed Choice Quantum Eraser by Johannes Fankhauser:
The lens in front of detector D0 is inserted to achieve the far-field limit at the detector and at the same time keep the distance small between slits and detector.
So the reason is that using the lens allows them to keep D0 closer to the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/553103",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Question about an Exercise with Time-Dependent Hamiltonian I've been recently been assigned this exercise:
Consider two spin 1/2 particles which are coupled through a time dependent interaction:
$$ H(t) = a(t) s_1 \cdot s_2 $$
where $a(t)$ is a function which is constant in the interval $[0,T]$ and zero elsewhere.... | You are right that at $t=0$ the system is still in state $|+,-\rangle$, since $a(t)=0$ for $t<0$ and this state is an eigenstate of the Hamiltonian. However, for $t>0$ it is not an eigenstate anymore, but a superposition of the two eigenstates $|1,0\rangle$ and $|0,0\rangle$. Each of these evolves with different time e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/553256",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why is surface tension measured in units of milliNewtons per meter? Rather than square meter(s)? Why is liquid surface tension written in units of mN/m, or milliNewtons per meter?
The related concept of surface energy for solids uses units of milliJoules per square meter.
| You're correct that the two concepts are indeed representing the same quantity. If the surface tension of a surface is $T$ then it would need $T l dx$ amount of work to move its boundary of length $l$ by a distance $dx$. Since $l dx$ would be the increase in area $dA$, the amount of work needed to increase the area of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/553657",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
How does a water jet hitting a wall move parallel to the wall if momentum is conserved? Classical mechanics says that if I throw a ball with velocity perpendicular to the wall and it collides elastically with the wall with a velocity $v_0$, then it bounces back with the same velocity $v_0$.
However, if I shoot a beam ... | If a tennis ball hits a wall, it bounces normally, but with several balls in a continuous jet, the outcome is different. Many bouncing balls will hit incoming ones, and the result will be a scattering pattern. The advantage of the direction parallel to the wall is that it is a free path from new coming balls.
I think ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554097",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 0
} |
Examples of path integral where path of extremal action does not contribute the most? I have learnt that by doing a saddle point approximation in the path integral formulation of quantum mechanics, the classical action (extremal action where $\delta S=0$) is the one that contributes the most, hence seeing how classical... | The answer by @Accidental FourierTransform has already mentioned the instantons, but let me give a more pedestrian example and a more pedestrian view on the question.
When we use a path integral to describe the motion of a single quantum particle, the saddle point approximation corresponds to what is otherwise known as... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554165",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 2,
"answer_id": 1
} |
Is this a typo in Peskin's QFT? In ''An intro to QFT (2018)'' chapter 3, Peskin does the following:
Let me introduce some notation first, let $v^s_k=\begin{pmatrix}\;\;\,\sqrt{k\cdot\sigma}\,\xi^{-s}\\-\sqrt{k\cdot\bar{\sigma}}\,\xi^{-s}\end{pmatrix}$ be a bispinor for the negative-energy solution to the Dirac eq. with... | Schwartz uses negative signature, so $(-i\gamma^2)^2=1$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554418",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Green Function in Open Quantum Systems Imagine an open quantum system interacting with an environment that admits a density matrix (Markovian) description in terms of Lindbladians ($c$ and $c^\dagger$). Is there a meaningful way to define a single particle Green function for this system up to the time the steady state... | Certain open system processes can be described within the Greens function formalism by adding imaginary terms to the Hamiltonian, namely all processes where something only exits the open system and nothin comes back from the environment. So, basically decay processes. Other non-unitary processes such as dephasing canno... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554506",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
"answer_id": 2
} |
Why do scientists need to measure extremely small intervals of time? Why do scientists need to measure extremely small intervals of time? Why is it necessary?
| It all depends on the phenomena one is studying. If you need to make an analysis about the general pick up of a car engine, i.e. how much time it take to go from 0 to 100 Km/h, one does not need to bother about femto-seconds rather seconds will suffice. However, for the time scales involved in atomic transitions or sub... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554707",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Is my friend right about omitting $c^2$ in world famous tiny equation? I know $E = mc^2$ says that inertial mass of a system is equal to the total energy content of a system in its rest frame. My friend told me the $c^2$ can be omitted from this equation because that's just an `artifact' when measuring inertia and ener... | It is very common to "omit" constants, especially in theoretical physics.
Actually, there is a system based only on physical constants ($c,\hbar,\epsilon_0,G ...$). Physical units in this system are called natural units and we can "normalize" those constants by choosing a system in which their value is 1, they are call... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554935",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 6,
"answer_id": 3
} |
$\gamma_5 \gamma^\sigma$ expressed with Levi-Civita tensor We have that $\gamma_5 = -\frac{i}{4!} \epsilon^{\mu \nu \rho \sigma} \gamma_\mu \gamma_\nu \gamma_\rho \gamma_\sigma$. Using this, what approach would be suggested in showing that $\gamma_5 \gamma^\sigma = \frac{1}{3!} \epsilon^{\mu \nu \rho \sigma} \gamma_\mu... | Indeed, you are right that conflating a saturated dummy index with a free index makes not sense.
However, you know that
$$
\gamma_5 \gamma^\kappa= \tfrac{1}{2}[ \gamma_5 ,\gamma^\kappa ],
$$
so what happens if you substitute the quadrilinear expression in the commutator? You know the leading, quintilinear, term vani... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555034",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is this formula I derived for net acceleration correct? I was thinking about acceleration due to gravity and I thought of deriving a formula that gives the net acceleration due to gravity between two bodies. Now, by net acceleration, I basically mean the effective acceleration. Please have a look :
Let $A$ and $B$ be... | Your formula is just fine. You can read about the "2 body problem" and solve it entirely.
You seem to be upset about that the relative acceleration depends on both masses, but is correct.
Think of $m_2$ >>> $m_1$. You get $g_1$ >>> $g_2$. You can aproximate relative acceleration by $g_1$ and
the acceleration of $m_1$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555203",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Acceleration as a function of position and time I know if you have an acceleration as a function of $t$, $a(t)$, to find the velocity you simply integrate $a(t)$ with respect to $t$. Moreover, if the acceleration was a function of position, $a(x)$, you use the fact that $a(x) = v(x) \cdot dv/dx$ and solve for $v(x)$. H... | the acceleration a is:
$$a(t)=\frac{dv(t)}{dt}$$
thus:
$$v(t)=\int a(t)\,dt+v_0\tag 1$$
if $a(t)\mapsto a(x(t),t)$
you get from equation (1)
$$v(t)=\int a(x(t),t)\,dt+v_0$$
and $x(t)$ is the solution of the differential equation $\ddot{x}=a(x(t),t)$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555315",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Does tangential acceleration change with radius? Do tangential velocity and tangential acceleration change with radius (change of radius on the same object)?
For example consider a spinning disk. Does the equation $$a_t = \alpha R$$ (where $a_t$ is the tangential acceleration, $\alpha$ is the angular acceleration and ... | A note on the case you're considering:
A disk is an extended body. This means it's a collection of points: and must be treated as such. To speak of the displacement/velocity/acceleration of a point on the disk and of the disk itself - the center of mass of the disk - are two distinct analyses.
Particles on the disk
Pa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555649",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
Why X-ray and radio waves can penetrate walls but light can not? Why can visible light, which lies in the middle between X-ray and radio waves in terms of frequency/energy, not penetrate walls?
| The interaction of photons with matter is complicated. The electromagnetic spectrum covers many orders of magnitude in frequency and photon energy, and there are qualitatively different processes that occur in different regimes. The results depend on the electrical properties of the material, such as conductivity and p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555778",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular? During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular to the original direction of the particle-antiparticle pair?
There is very little information on the web about this topic, though I rea... |
During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular to the original direction of the particle-antiparticle pair?
No.
In the center-of-momentum frame, the two photons can come out back-to-back in various directions, with a probability distribution. Any direction is consistent wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555916",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
Does putting a thin metal plate beneath a heavy object reduce the pressure it would have applied without it My dad bought an earthen pot and he kept it on our glass table. Worried that the glass could break on filling the pot with water. I kept a metal plate beneath it. At first, it seemed like a good idea , but on fur... | I don't think a metal plate is necessary for a thick glass like that, supported by an wood table.
Being transparent, glass looks like more fragile than it actually is.
I have a ceramic floor for example. Each ceramic plate has 60 x 60 cm, and much thinner than the glass of the picture. Moreover, the contact with the co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556175",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 1
} |
Does the angular velocity of a spinning disk increase if it has a completely inelastic collision with a object with a greater tangential velocity?
A roller of radius 10cm is spinning with a angular velocity of 15 rad/s. It has a completely inelastic collision with a hunk of clay, with mass m moving at 3m/s at it's ver... | Angular momentum is conserved in an inelastic collision, so all you have to do is calculate the total angular momentum of the system the moment before the collision and the moment after. Before the collision, the total angular momentum is the sum of the angular momentum of the roller and the angular momentum of the cla... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556263",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why is the morse potential shifted for two different electron energy levels? I saw this image from the Wikipedia article on the Franck-Condon principle:
But couldn't find an explanation for the shift $q_{01}$ to the right (i.e. increasing the inter-nuclear distance) as the electron energy level goes from $E_0$ to $E_1... | There is no reason why equipotential curves should have their minima lined up at the same internuclear distance or why the shapes would be similar.
As an example, when in a single-electron picture an electron is excited from a bonding orbital to an antibonding orbital, if there still is a minimum, it would be at a larg... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556381",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What would this inclined force equate to? In the attached problem, i'm curious what effect, if any, the incline would have on the torque generated by the 50 kips force (shown below). Would it lead to a smaller/larger torque and, if so, why? I think the incline wouldn't influence torque necessarily, since the angle bet... | The incline should not affect the torque. The torque of the 50 kips force (F) should be T = hxF, where h is distance AC. To calculate force of 60 kips force (F1) you will need to project the force vector outward so that it can form a line that is perpendicular from A to that point (supposing A is the pivot) if not is t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556512",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Applying the principle of Occam's Razor to Quantum Mechanics Wolfgang Demtröder writes this in his book on Experimental Physics,
The future destiny of a microparticle is no longer completely determined by its past. First of all, we only know its initial state (location and momentum) within limits set by the uncertain... | Further to the points discussed, the relevant principle when comparing theories of different empirical success isn't Occam's razor, but the correspondence principle. Originally that refers to quantum mechanics recovering classical mechanics in a certain limit, but more generally it means a new theory is accepted when i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556585",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 10,
"answer_id": 2
} |
What's the debate about Newton's bucket argument? I visited some other QA threads about this topic, and I don't understand why people think it's mysterious that the bucket knows about its rotation.
If a non-rotating bucket is all there is in the universe, then, initially, all the parts of the bucket are at rest wrt to ... | In Newtonian mechanics (and also relativity and quantum mechanics), a hypothetical physicists sitting in the bucket would definitely be able to do an experiment to detect that the bucket is rotating. I'm not sure why that would be mysterious. It should be noted that the velocities of the particles involved (relative to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556759",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
What does the Problem 14 from Goldstein's book on classical mechanics chapter-7 (special relativity) really mean? I am having difficulty in understanding problem number 14 in Goldstein's Classical Mechanics, 3rd edition, chapter 7 on special relativity. Here is the problem ---
A rocket of length $l_0$ in its rest syst... | I'd like to add to what 'PM 2Ring' wrote. The observer will measure the rocket to have a constant length no matter where it is in the observer's frame of reference (assuming it is moving at a constant velocity -- in which case it will be length contracted).
However, the observer will observe the rocket to be longer wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556910",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Topological Insulator - why does a band have to be isolated to have a Chern number of 1? I'm trying to understand the principle of topological insulator.
Why a band has to be isolated to have a Chern number of 1? More precisely, why, in the case of Haldane Model, all the bands in the valence band don't participate with... | There's an intuitive answer and a mathematical answer. Mathematically, the Chern number is defined as $\frac{1}{2\pi i}\int\epsilon^{ij} \langle\partial_i u|\partial_j u\rangle$. Thus, it requires you to have $|u\rangle$ be a locally differentiable function of $k$. But if a band touches another band, $|u\rangle$ can ch... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/557128",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why don't hovercrafts move West relative to the Earth Suppose that there is a hovercraft floating a few centimetres above the Earth's surface. As it is disconnected from the Earth, which is spinning from West to East, shouldn't it appear to move East to West to observers on the ground? Does this happen? If not, why not... | Compare the case of a plumb line. Anywhere on the planet a plumb line will hang perpendicular to local level surface. This is true both on a planet that is rotating, such as our Earth, and on a planet that is not rotating.
The Earth rotates at a constant angular velocity. For any object that is co-rotating with the Ear... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/557462",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
How does the reversibility of physics interact with nuclear fission? The laws of physics are reversible and quantum information is never destroyed.
Given this, how do I time reverse the $U_{235}$ fission reaction, n which
${}^1_0n + {}^{235}_{92}U \rightarrow {}^{141}_{56}Ba + {}^{92}_{36}Kr + 3 {}^1_0n + \gamma +$ 202... | The reverse reaction really is
$${}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + 3\ {}^1_0n + \gamma + 202.5\ \mathrm{MeV} \rightarrow {}^1_0n + {}^{235}_{92}\mathrm{U} $$
as you'd expect. Yes, your deduction from time symmetry is absolutely correct (as far as we know) - it has to be. The above will do the job. Ye... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/557614",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why do peaks and troughs of a wave cancel each other out? And why peaks and peaks or troughs and troughs add up? I have thought that the cancellation of peaks and troughs is a consequence of Newton's third law of motion that equal and opposite forces cancel each other out.
Or it has something to do with conservation of... | Mathematically it can be seen as a consequence of waves obeying a linear second order differential equation.
Physically, for mechanical waves, it’s the fact that forces are additive that result in the addition (superposition) of waves. This means that if two forces are acting at a point, then the net force that acts is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/557719",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why doesn't water boil in the oven? I put a pot of water in the oven at $\mathrm{500^\circ F}$ ($\mathrm{260^\circ C}$ , $\mathrm{533 K}$). Over time most of the water evaporated away but it never boiled. Why doesn't it boil?
| It might also be prudent to consider the environment of the oven itself. The "atmosphere" in the oven is already at a temperature > 100°C and this means that water in the "air" is in the gaseous state. As water evaporates at the surface at temperatures nominally > 40°C this would mean that the water vapour is "immediat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/557812",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "139",
"answer_count": 7,
"answer_id": 4
} |
What is the torque produced by 2 rotating bodies with a clutch I am trying to simulate a car engine etc, but I have failed to find any equations governing the torque created by $2$ different constant velocity shafts of different angular momenta joining together with some given slip or friction factor. I know $I_1w1 + I... | In a system with two drive shafts connected by a clutch and a system of gears, the power being transmitted by each shaft will be the torque times the angular velocity. (The angular momentum of each shaft is not of concern.) The ratio of the two angular velocities is determined by the system of gears. The clutch allows... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/557938",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Why does bottle with long straw get emptied first? Two identical bottles with different straw length are filled with identical liquids (obviously up to the same height as depicted in the picture). Bottle with long straw is emptied first.What can be it's possible reason?
| In a fluid like water or air, the pressure $P$ and velocity $v$ depend on the height $h$ and density $\rho$ in a way described as the Bernoulli equation,
$$
P + \frac12 \rho v^2 + \rho g h = \text{constant}
$$
In your setup, the opening of the straw and the upper liquid surface at the base of the bottle are both open t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558072",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why do we describe probability amplitude rather than probability itself in quantum mechanics? In the quantum mechanics, the dynamics of quantum system are described in terms of probability amplitude. However, we want to calculate the probability in the end which can be measured. Why don't we develop quantum mechanics d... | To make sense of interference fringes without probability amplitudes, you would need a messy ad-hoc theoretical framework like the Bohmian pilot wave. Probability amplitudes are used simply because it explains interference in a simple way
$$P_{A+B} = (\langle \Psi_A | + \langle \Psi_B | )(| \Psi_A \rangle + | \Psi_B \r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558181",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why exactly do we feel a shock when we place our hand into a conducting solution? I have a very naive question.
Suppose you have pure water in a flask, and you place two ends of a copper wire (which are connected to a battery) into the water.
If you were to place your hand into the water, you would not feel any shock, ... | If I may ask, why do you feel a twinge when you step on a nail or a pin pricks you? The same way your nerves make you feel the painful sensation of stepping on a nail is the same way that they react when current flows through your hand. It's not that current flows through your body but how your nervous system reacts to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558308",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Oscillations of Dielectric Slab in Parallel plate capacitor In the book Principles of Physics by Resnick Halliday:
The decrease in Potential energy of a parallel plate capacitor due to a dielectric is because the slab would start to oscillate and the energy would transfer back and forth between the kinetic energy of th... | The point is that there are two ways of insertion that is with constant potential difference maintained where it doesn't depend on x so it is periodic not shm but in 2nd case it will perform shm as it is dependent on x and directly proportional
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558400",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Does it make sense to say that something is almost infinite? If yes, then why? I remember hearing someone say "almost infinite" in this YouTube video. At 1:23, he says that "almost infinite" pieces of vertical lines are placed along $X$ length.
As someone who hasn't studied very much math, "almost infinite" sounds like... | In physics if a quantity, call it $\lambda$, in a theory was said to be "almost infinite", I would interpret this as stating the effective theory obtained by taking the limit $\lambda \to \infty$ is accurate up until some very long length scale or time scale after which it breaks down.
Crucially this breakdown length/... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558491",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 11,
"answer_id": 2
} |
Why is the electric dipole moment parallel/antiparallel to angular momentum? In several textbooks and papers, like this one for example, a claim like the following is made:
The EDM of a system $\vec{d}$ must be parallel (or antiparallel) to the average angular momentum of the system $\hbar\langle\vec{J}\rangle$.
What... | They are probably talking about the quantum mechanical expectation value, which has to be along the angular momentum vector. If the angular momentum is zero, the expectation value of any vector would be zero.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558798",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Yo yo motion and energy conservation I am struggling with balancing energy in a yo-yo. So, we have a yo-yo (massless string wrapped around solid cylinder). It is allowed to fall through a distance $h$ without rotation. The loss in potential energy $= mgh$ will be converted into kinetic energy (KE) and we can find the K... | Obviously, the yo-yo's energy has to be conserved. The potential energy of the yo-yo at the stationary starting point where it starts to move down ($mgh$, $h$ being the length of the rope) is converted in a linear and a rotational kinetic energy part (as you wrote). The linear acceleration downwards though is less than... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/558898",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is the Topologically Twisted Index? I know that one can take a supersymmetric theory defined on $\mathbb{R}^n$ and topologically twist it by redefining the rotation group of the theory into a mixture of the (spacetime) rotation group and the R-symmetry group. However, what I'm a bit confused about is: what is a t... | It would be great that you sharpen your question by asking for a specific case.
But the general intuition is as follows: In a non-twisted theory, an index compute the dimension (possibly the virtual dimension) of the space of solutions of some differential equations that preserve some amount of supersymmetry.
Twisted t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
One-loop Feynman integral over Euclidean momenta I am trying to perform the following one-loop computation
$$
\int \frac{d^Dq}{(2\pi)^D} \frac{(k+q)^2 q^2}{((k+q)^2+m^2)(q^2+m^2)}
$$
where $k$ is fixed and everything is on the Euclidean setting, so there is no need to perform any Wick rotation.
I can not find the solut... | This question is a couple years old, but I ran across it in a search, and it has a fairly simple answer. The trick for dealing with the numerator is
$$\int \frac{d^Dq}{(2\pi)^D} \frac{(k+q)^2 q^2}{((k+q)^2+m^2)(q^2+m^2)}=\int \frac{d^Dq}{(2\pi)^D} \frac{((k+q)^2+m^2-m^2)(q^2+m^2-m^2)}{((k+q)^2+m^2)(q^2+m^2)}$$
$$=\int ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Describing forces in rolling Consider a wheel on a frictionless horizontal surface. If we apply a horizontal force (parallel to the surface and above the level of the center of mass), what happens to the wheel? Does it roll or slide forward or rotate only or does any other phenomenon happen? Please guide me. Also draw ... | It should roll. Whether it will be rolling with sliding or pure rolling we don't know until we know what height the force was applied at.
Breaking the motion into Translation and Rotation, we can write one force and torque equation each for both respectively as such-
$F=ma$
$ \tau=I\alpha=rF$
We can also calculate the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559470",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
What is happening when magnetic field lines snap or break? In discussions of sun spots and auroras on Earth, magnetic field lines are often described as "snapping" or "breaking", with the result of releasing charged particles very energetically.
My understanding is that field lines are just a visualization tool. I don'... | I simulated two bar magnets with 4 dipoles each and plotted the field lines and field intensity around them.
Here is what I observed.
I noticed that the dipole chain forms a set of null spots in the field on either side of the chain. As the magnets are pulled apart, two of these null spots (green dots) move away from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "55",
"answer_count": 5,
"answer_id": 4
} |
Why use virtual displacement to make constraint forces vanish? Why do we use virtual displacement to vanish work done by constraint forces instead of the actual displacement?
| H. Goldstein, Classical mechanics, Chapter $1$ says
"Note that if a particle is constrained to a surface that is itself moving in time, the force of constraint is instantaneously perpendicular to the surface and the work during a virtual displacement is still zero even though the work during an actual displacement in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559861",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Instantons in 1+1 dimensional Abelian Higgs model Let's consider the Abelian Higgs model in 1+1 dimensions in Euclidean space-time:
$$L_E=\frac{1}{4e^2}F_{\mu\nu}F_{\mu\nu}+D_\mu\phi^\dagger D_\mu\phi+ \frac{e^2}{4}(|\phi|^2-\zeta)^2$$
where $\zeta>0$ and $D_\mu\phi= (\partial_\mu-iA_\mu)\phi$.
We are looking for finit... | Advanced Topics in QFT (Shifman) talks about U(1) anomaly in 1+1, Aspects of Symmetry (Coleman) have topics on Higgs 1+1, and probably something about it in David Tong lectures.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/559969",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Wick theorem exercise I'm a newbie in QFT and I have some doubts with this simple exercise:
Using the Wick Theorem evaluate
$$\langle0|T(\phi^4(x)\phi^4(y)|0\rangle$$
*
*Use a diagrammatic approach to represent the possible contractions
(how many $\phi$-lines are attached to each vertex).
*Determing numerical facto... | First of all the Wick's theorem states
$$
T(A B C \ldots Y Z)=:\{A B C \ldots Y Z \,+"\text { all contractions" }\}:
$$
(In the case of fermions we have to take care about anticommutation relations,
i.e. every time when we interchange neighboring fermionic operators a minus sign appears.)
In this exercise you shall app... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is it possible for two observers to observe different wavefunctions for one electron? Suppose there are 2 scientists who have decided to measure the location of an electron at a same fixed time. Is possible that while one observes the wavepacket localized at (position=x) while the other observes the wavepacket localize... | The OP specified that the two observers make their measurements simultaneously. Two simultaneous measurements of the same observable are equivalent to a single measurement, which can have only one result. Therefore, the observers must see the same result.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560201",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Why does the entanglement of quantum fields depend on their distance? When watching Seans Carrol's "A Brief History of Quantum Mechanics", he mentioned around the 50th minute (the video I linked to starts at that point) that
[about quantum fields in vacuum] ... and guess what! The closer they are to each other, the mo... | I expect that Carrol is referring to cluster decomposition, a principle satisfied by many quantum field theories. This principle says that if two quantities are located in spacelike-separated regions very far from one another, then they are going to be uncorrelated. That is, if operators $A$ and $B$ are localized in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560399",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 0
} |
Cold neutrinos - how are they distributed? Cold or slow neutrinos have non-relativistic velocities and hence very low energies. That makes them very difficult to detect. Answers to Where are all the slow neutrinos? make it clear that they are vastly abundant. Do we have any significant model of how they are distributed... | We do have a model which gives the proportion of energy density the neutrinos occupy in the universe, the standard cosmological model or $\Lambda$CDM model. Neutrino number density is given by integrating the Fermi-Dirac distribution over the momentum space:
$$
n_\nu = n_s\int\frac{d^3p}{(2\pi)^3}\frac{1}{e^{p/T_\nu}+1... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560542",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 2,
"answer_id": 1
} |
Invariance of Lagrangian under rotations in a constant magnetic field
The Lagrangian for the motion of a particle with mass $m$ and charge $q$ in a constant magnetic field $B$ is given by $$\mathcal{L}(x,v)=\frac{m}{2}\left|v\right|^2-\frac{q}{2c}\left(v\cdot[x\times B]\right).$$
Show that rotations around the $B$-axi... | The conservation of the second term seems intuitive, as simply a preservation of volume, formed by vectors $v, x, B$. Nevertheless, I also present a way to deduce this for infinitesimal transformation, which will imply for a finite rotation. Under a small rotation with $\eta \ll 1$, the variation of vector $a$ is $\del... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561221",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Why do reflection gratings work? The law of reflection (that the angles of incidence and reflection are equal) can be derived directly from Maxwell's equations, or from Fermat's principle. However, reflection gratings completely defy this law, and from light incident at a fixed angle comes a whole diffraction pattern -... | A reflection grating is not a mirror. It is an array of reflective grooves in a surface. Light reflected from the bottoms of the grooves is delayed relative to light reflected from the tops of the grooves, just as light transmitted through optically thick portions of a transmission phase grating is delayed relative t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561487",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is a capacitor a dipole? A few more questions about understanding dipoles I recently learned about dipoles, according to its definition I was wondering if a capacitor can be considered also as a dipole?
Also I was wondering what is the physical meaning of the dipole moment $\vec{p}=qd$?
And my last question is what is ... | Since we believe that the universe is electrically neutral, any separation of positive and negative charges can be considered as a combination of electric dipoles.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561873",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Why can't primordial fluctuations be super-"horizon" without inflation? I am trying to understand why, in cosmology, it is said that the presence of fluctuations at scales above the Hubble distance would not be expected in the absence of inflation or something like it.
We treat density fluctuations using the density co... | You can have field fluctuations on any scale, but in a non-inflationary spacetime they just return to the vacuum. You need inflation to convert the fluctuation to a classical curvature perturbation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562002",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How can we conclude from Maxwell's wave equation that the speed of light is the same regardless of the state of motion of the observers? I am reading a book titled "Relativity Demystified --- A self-teaching guide by David McMahon".
He explains the derivation of electromagnetic wave equation.
$$
\nabla^2 \, \begin{case... | If Maxwell's equations have the same form in all frames of reference, then the wave speed is defined by the product of two physical constants, irrespective of coordinate system. i.e. Your book just implicitly assumes that, but of course it requires experimental testing - i.e. Michelson-Morley etc.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562149",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "30",
"answer_count": 6,
"answer_id": 4
} |
Do atoms absorb the same amount of light? I'm currently working on a project on my own where I'm interested in finding information about an object based on a spectrum. Namely, I want to use the spectrum that I input into my program to be able to analyze what atoms are present in the analyzed object. (I know this is pro... |
Do atoms that are exposed to the same amount of light absorb the same
amount as well?
The question is a little fuzzy, so let's try an be more concise.
Take sodium ($\text{Na}$), famous for its strong, yellow doublet emission line.
In identical conditions all sodium atoms emit the same intensity of that yellow doublet... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562229",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Baryon number vs electromagnetic charge, what is the difference? What exactly is a Baryon number? I looked up definition from wikipedia and still struggle to understand this. And how does this differ than the
electromagnetic charge?
My textbook did the following computation:
It is calculating the electromagnetic charg... | A baryon is any particle held together by the strong force (i.e. a type of hadron) that comprises three quarks. An antibaryon has three antiquarks.
The baryon number $B$ is just the sum of all the quarks $n_q$ minus the sum of all the anti-quarks $n_{\bar q}$ :
$$ B = \frac{1}{3}(n_q-n_{\bar q}).$$
So, a quark has bary... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562307",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
In metals, the conductivity decreases with increasing temperature? I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.2 Material equations says the following:
Metals are very good conductors, bu... | The characteristic feature of metals is that the valence electrons of the atoms delocalise across the crystal lattice- this is an intrinsically quantum mechanical phenomenon. In essence, the electrons propagate as plane waves and this delocalisation lowers the energy of the electrons. As you increase the temperature, v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562392",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 1
} |
Why Ohm’s law doesn’t work in these scenarios (inside ideal battery and in vacuum)? Scenario 1 - Ideal battery
Suppose I have an ideal battery whose electrolyte’s resistance is zero. In the working battery there will be current flowing inside the battery also (due to battery forces) from lower potential to higher poten... | Despite the name, Ohm’s law is not a general law of nature. It is instead a defining characteristic of a small class of materials and devices called resistors (and conductors). Ohm’s law does not apply to other materials and devices, including insulators, capacitors, inductors, switches, transistors, vacuum, voltage so... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562633",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Capacitance of ferroelectric capacitor in saturated regime Consider a ferroelectric plate capacitor connected to an AC source in the presence of a strong static external electric field which sets the ferroelectric medium in the saturated regime.
The question:
Does the static polarisation $P$ of the ferroelectric have a... | Your second approach is correct.
There are a few problems with the first one. First of all, $Q=CV$ no longer applies, because when you have no charge on the capacitor, there is still a non-zero E-field within the ferroelectric, and thus a non-zero potential difference across the capacitor plates. The appropriate defini... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562814",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How is the frequency of a wave defined if it propagates on three different directions? Let's consider a wave which propagates on 2 or three directions, like for instance an electromagnetic wave inside a rectangular waveguide totally closed on two ideal conductor surfaces:
The walls of the guide force the wave to assum... | The frequency is, as always, the number of cycles per second of the oscillations. It is related to the spatial wavelength by $f = \frac{c}{2 \pi} |\vec{k}|$, where $c$ is the speed of propagation of free waves in the medium and
$$
\vec{k} = (k_x, k_y, k_z) = \left( \frac{2 \pi}{\lambda_x}, \frac{2 \pi}{\lambda_y}, \fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Pseudo Force and Inertial and Non-Inertial frames In the figure given below is block placed on an incline $\theta$. Now the lift is accelerating upwards with an acceleration $a_0$. Now if we make our measurements from the lift frame we will have to apply a pseudo force $-ma_0$. Which will have two components one in the... | The acceleration of the mass, a, in the inertial frame is the sum of the acceleration of the elevator, $a_o$ and the acceleration of the mass relative to the incline, a', in the elevator. To avoid using the normal force, I'll chose the +x axis parallel to and up the incline. Then for x components: -mg sin(θ) = m$a_x$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563437",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 5,
"answer_id": 3
} |
What do $\ell$ and $A$ precisely mean in the formula for electrical resistance? The formula for resistance is
$$R=\rho\frac{\ell}{A}$$
Generally in most of the textbooks it simply written that $\ell$ is the length of the conductor and $A$ is it’s cross-sectional area. But my question is which length and area do we need... | In the formula the area(A) is perpendicular to the flow current,
The length (l) is along the flow of current.
Consider an example that will clear you doubt.
Consider a hollow cylinder with inner radius 'a' and outer radius 'b'
and length 'l' .
Case 1- Potential difference is applied along the length 'l' of cylinder.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/563802",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
Does tau decay to rho meson + tau neutrino? In the particle data group table: http://pdg.lbl.gov/2020/tables/rpp2020-sum-leptons.pdf ,only $\tau \rightarrow \pi + \nu_{\tau}$ is documented. But does $\tau \rightarrow \rho + \nu_{\tau}$ as well? I don't see any conservation laws that could forbid such decay to happen.
| The $\rho$ has the quantum numbers of $\pi\pi$ coupled to $I=1$. If they only list particles stable under the strong interaction then $\tau^-\to\rho^-\nu$ is the same as $\tau^-\to\pi^-\pi^0\nu$, which indeed has a branching ratio of 25%. The table is more helpful than that: It lists the non-resonant (non $\rho$) part ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564093",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why is internal resistance of battery considered outside the terminals although it is present between the terminals inside the battery In ideal battery the internal resistance is zero whereas in non-ideal battery there is some internal resistance now this internal resistance is due to the battery material (electrolyte)... |
Why does one represent the internal resistance of a non-ideal battery as external?
It is just a way of representing a non-ideal battery. Wherever the battery goes, the resistance goes with it, then why worry if one is showing it inside or outside. It will be considered in the Kirchhoff's voltage law anyhow.
An uncann... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564196",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 6,
"answer_id": 4
} |
Finding acceleration of center of mass in cart pole problem In this link about finding equations of motion of cart pole problem,
There is an equation about acceleration of center of mass of the pole.
Screenshots of them below.
I don't understand why they have more than two parts about angular acceleration - $\varepsi... | That last term is the centripetal acceleration associated with the rotation of the rod.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564395",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Work Equals Torque? Horsepower, Pulleys While reading one definition of torque, I saw its units are Newton-meter, which is the same as work. But sources usually make it a point to emphasize "even though both work and torque units are the same, they should not be confused, they are very different". One is like an objec... | This is a little bit of a pet peeve of mine, so I’ll chime in with my two cents / rant.
Torque and work don’t actually share the same units, torque actually has units of $\frac{\mathrm{N\,m}}{\mathrm{rad}}$. Dimensionally speaking, the distinction is irrelevant because radians are dimensionless, however most formulas f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564843",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 1
} |
How do balances (not scales) work? More specifically, why does having two objects of different weights make the balance lean to one or the other then stop partway? Why does the balance not just keep tilting until it falls to the side? How can something be heavy enough to tip the balance but not heavy enough to make it ... | Balances work because they only need to tell when things are in balance, not how far out of balance they are. As such, the only behaviors needed are those which are very close to equilibrium.
When one is that close to equilibrium, small things matter. For example, as you tip, you roll the fulcrum ever so slightly to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/564981",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Newtonian Limit of Schwarzschild metric The Schwarzschild metric describes the gravity of a spherically symmetric mass $M$ in spherical coordinates:
$$ds^2 =-\left(1-\frac{2GM}{c^2r}\right)c^2 \, dt^2+\left(1-\frac{2GM}{c^2r}\right)^{-1}dr^2+r^2 \,d\Omega^2 \tag{1}$$
Naively, I would expect the classical Newtonian limi... | Consider the change of coordinate
$$r=r'\left(1+{{\cal G}m\over 2r'c^2}\right)^2={r'}^2(1+U)^2$$
where $U={\cal G}m/2r'c^2$. One can check that
$$1-{2{\cal G}m\over rc^2}=1-{2{\cal G}m\over r'c^2(1+U)^2}
={(1-U)^2\over (1+U)^2}$$
Moreover,
$${dr\over dr'}={d\over dr'}\left[r'\left(1+{{\cal G}m\over 2r'c^2}
\right)^... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565070",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
In what sense are spin coherent states "classical"? Spin coherent states are often introduced as "the most classical states of a finite-dimensional system", or as the analogous of coherent states of light for finite-dimensional systems. See e.g. (Radcliffe 1971) and (Chryssomalakos et al. 2017).
One way to define them ... | *
*They saturate the "displaced" uncertainty relation. If
\begin{align}
\vert \Omega\rangle=R(\Omega)\vert jj\rangle
\end{align}
is the coherent state, and
\begin{align}
J_k^\prime=R(\Omega)J_kR^{-1}(\Omega)
\end{align}
for any rotation $R(\Omega)$, then
\begin{align}
\Delta J_x^\prime \Delta J_y^\prime=\frac{1}{2}\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565127",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 0
} |
Are there any quantum effects which we can see in every day life? I am wondering if there are any natural phenomenon in every-day life that cannot be explained by classical physics but can only be explained by quantum mechanics. By classical physics, I mean Newtonian mechanics and Maxwell's electromagnetic theory.
I kn... | In addition to the other answers, it is also true for ferromagnets, the strong magnetism is explained by the means of exchange interaction. With the machinery of QM one explains the hysteresis and formation of magnetic domains. The weak magnetism, paramagnetisim and diamagnetism can be explained on a classical level.
T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565248",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 9,
"answer_id": 3
} |
In the generation of X-Rays, why the incoming electron generated from anode knocks out the K shell electron rather than outer shell electrons? When the high energy beam of particles or photon hits the cathode, electrons from $K$ shell are knocked in the generation of characteristic x-rays. Why do inner electrons get kn... | Interactions of electrons with atoms needs a quantum mechanical formulation, classical electrodymics, where bremsstrahlung and synchrotron radiation of X-ray energies can be modeled is not enough to model X-rays from atoms. As Farcher shows in another answer the quantized nature of the energy levels of the electrons h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565443",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Derivation of non-linear Schrödinger equation from many-body QM I hope this (and not MathOverflow) is the right place to post this question. I am a math student taking a methods of mathematical physics course, in which we cover the solution theory the non-linear Schrödinger equation $$i u_t+ \frac{\Delta}{2}u=\lambda|u... | The derivation is in the paper by Pitaevskii posted in the comment above.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/565590",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why are there no operators in classical mechanics? I have been wondering to find the answer of some fundamental questions in quantum mechanics and the answer to the above question will help me to clear doubts of quantum world
| Operators do exist in classical physics. The thing is, we don't use them in the same way.
In mechanics, for example, compute the eigenvalues and eigenvectors of an operator is important to study vibrational modes. You also can find examples of diagonalization of operators in electrodynamics and heat propagation.
Diagon... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566063",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Impulse operator on real wave function The impulse operator in quantum mechanics is given by
\begin{align}
\hat{p} = \frac{\hbar}{i}\nabla
\end{align}
As a Hermitian operator, the expected value of this operator $\langle{p}\rangle = \langle \psi|\hat{p}\psi\rangle$ should be real. However, for a real wave function $\ps... | Just to add to Vadim's answer: The integral
$$\int_{-\infty}^{\infty} \psi \partial_x \psi dx= \frac12 \int_{-\infty}^{\infty} \partial_x( \psi^2) dx = [\psi^2]_{-\infty}^{\infty}=0
$$
fo all wavefunctions that vanish at infinity.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Measuring the Hubble constant in a curved universe In an article from the University of Chicago, July 17, 2020, it is stated that
"Judging cosmic distances from Earth is hard. So instead, scientists measure the angle in the sky between two distant objects, with Earth and the two objects forming a cosmic triangle. If... | I guess you are looking for angular diamater distance. For different curvature the equation takes different forms. See here https://en.wikipedia.org/wiki/Angular_diameter_distance
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
If a pendulum of mass $m$ and length $l$ is considered quantum mechanically, what will be the approximate ground state energy? I have seen that the solution of the quantum pendulum is obtained by solving the Mathieu's equation form of the Schrodinger equation and it also depends on a parameter 'q' called the energy bar... | My best guess would be $\dfrac{h\nu}{2}$. Note that it requires quantum gravity to check my answer .
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566558",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Optics: mirrors While drawing ray diagrams for plane and spherical mirrors, what is generally taken as the point of observation?
Eg, If a concave mirror is presented with, say a wire turned into a triangle, placed from focus towards the mirror, the image can be obtained following rules of reflection but where would the... | In ray tracing, typically light rays leave a point of an object, go through an optical system, and pass through a point of an image.
Sometimes a detector is placed at the image. Different points of the detector see different points of the image. The outcome may be different pixels of a photograph.
In other cases, the l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566730",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Is this a kinematics paradox? You consider a shaft which can rotate freely (there will be of course a frame with ball bearing to hold the shaft firm and to allow it to rotate with low friction); fixed on this shaft there are two gears, one with radius $R$ and another with radius $2R$. Note that the two gears rotate tog... | By examining the gears on the left we can see that for every revolution of 1, 2 must undergo two revolutions. By examining the gears on the right we can see that for every revolution of 1, 2 must undergo half a revolution. This is not possible, so the gears will not turn.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566815",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 3
} |
Maximum velocity of elastic pendulum released from rest Consider the following problem.
Construct a pendulum with a mass $m$ at the end. However, we don't a rigid rod of length $\ell$, we instead use a spring of natural length $\ell$ and spring constant $k$. We lift the mass so that the spring is horizontal and at its... | You can construct a free-body diagram for the pendulum bob at the lowest point of its motion and balance out the forces in the vertical direction to obtain yet another equation.
The weight of the bob subtracted from the force on the bob due to the extension of the spring should provide the necessary centripetal force f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/566905",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having s... | The answers will differ, because the charge distribution on each sphere will not be uniform. Effectively, each sphere will have an induced dipole moment due to the presence of the other, which will change the force between them.
This effect of the charge distribution, however, will generally be smaller than the basic e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Will cutting sand paper with scissors make the scissors sharper or duller? This is a little question that I have been wondering when I need to cut sand paper with scissors.
Sand paper can be used to sharpen knives etc. when applied parallel with the blade surface. Also it can be used to dull sharp edges when applied no... | Sand paper removes material. When used properly, that removal of material can make a blade sharper. However, when cutting the sandpaper, there is no attempt to structure the removal of the material. It will simply dull the scissors. It will remove material in a relatively haphazard manner, taking off the sharp edge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567343",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 3,
"answer_id": 0
} |
Classical Wave theory and the photoelectric effect I read that according to classical wave theory, light is viewed as a wave whose intensity is continuously variable. And for this reason, it is unable to explain the photoelectric effect. My questions are:
*
*What does "continuously variable" mean?
*How does the int... | Measurements indicate that in the photoelectric effect, the energy of the electrons which leave the surface depends on the frequency of the incoming light, but not on the intensity of the light. This indicates that the incoming light consist of bundles (or quanta) of energy whose size is determined by the frequency. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567420",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Is the entropy of a rotating body largest when the axis of rotation passes through it's centre of mass? I am looking for an answer to the observation that a body always rotates about its centre of mass when freely tossed. It can be explained if the entropy is highest in the case when the axis passes through the com, ho... | This question is based on the false premise that an object has a unique axis of rotation. One can choose any point, whether inside, on, or outside the object, as the center of rotation. Pick some other point that is not on the resulting axis of rotation and you'll get another axis passing through that point that is par... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567558",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Is energy required in generating magnetic field in simple resistance circuit? Consider a simple resistance circuit with a cell and a resistor. It is stated that energy stored in cell appears as heat in resistance as current flows in ideal circuit (neglecting EM radiation) as whole.
POWER/RATE OF HEAT GENERATION = POWER... | I agree with the answer @Dale provided.
To put things into perspective, the energy stored in the magnetic field of a straight conductor is minuscule compared to the energy dissipated in the resistance of the conductor.
The inductance of a straight copper wire 1 mm in dia and 10 cm long is about 105 nH. The energy store... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567623",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Trying to understand a visualization of contravariant and covariant bases I was trying to intuitively understand the covariant and contravariant bases for a coordinate system and I came across this image on Wikipedia:
Edit: After reading the first two answers I think I may have not posed my question correctly so I hav... | It would be more intuitive if you look at the illustrations form Daniel A. Fleisch's book on A Student's Guide to Vectors and Tensors.
Here they are:
The parallel projections represent contravariant components of a given vector $\vec{A}$ and the perpendicular projections represent the covariant components of the giv... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567770",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 7,
"answer_id": 3
} |
Are there non-constant potentials that result in eigenstates of the Hamiltonian that are all plane waves? It is commonly known that the eigenstates to the Hamiltonian of a constant potential are plane waves, aka
$$
V(r) = V_0 \Rightarrow H\psi = n \text{ with } \psi = \exp\left(\frac{ip}{\hbar}x\right)\exp\left(-i\frac... | Plane waves are eigenstates of the momentum operator. Another observable can have the same eigenstates only if it commutes with the momentum operator (see this answer for more details).
Now, the momentum operator generates translations, so the Hamiltonian commutes with it if it is invariant under translations. The kine... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/567865",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.