Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Massless string vs massless spring in a mass-spring system
Two masses connected by a massless spring, on a frictionless surface , and a force of $60$N is applied to the 15kg mass such that it accelerates at 2 $\frac{m}{s^2}$. What is the acceleration of the $10kg$ mass?
I came across this question. I first thought ... | The problem is poorly stated. If a 60 Nt force is applied to a 15 kg mass, the acceleration will be 4 m/s/s. The 10 kg mass will start slowly and accelerate as the spring is stretched. The two masses will then oscillate relative to each other. At some later instant when the force from the spring is 30 Nt, the 15 kg ... | {
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"timestamp": "2023-03-29T00:00:00",
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Cars' wear resistance, quietness and water drainage dependence on thread pattern on tires? Why can tires with fine thread patterns increase cars' wear resistance, quietness and water drainage? What is the logic behind?
The following is the tire ad I saw:
Nowadays, under the premise of pursuing comfort, most of Sedan ... | Here is how this works. When a rubber tire rotates and comes into contact with the pavement, the round rubber tire gets deformed (pressed flat against the flat pavement).
Since the tire wants to remain round, this causes the tire surface to "scrub" against the pavement which grinds away at the tire surface, wearing of... | {
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What is the ideal damping ratio for a building? I am a high school student investigating how the mass ratio of a pendulum tuned mass damper inside a building (ratio of the mass of the pendulum tuned mass damper to the mass of the structure) affects the damping ratio when the building vibrates. How do I select the ideal... | The optimum damping ratio is that which produces a critically damped system. Critical damping dissipates the system energy in the shortest possible time and does not support oscillation. For a critically damped system, the damping ratio is equal to 1.
| {
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The fluctuation-dissipation theorem In Giuliani & Vignale's Quantum Theory of the Electron Liquid, in page 126, they point out that the absorption and emission spectra are related by $$S_{AA^\dagger}(-\omega)=e^{-\beta\hbar\omega}S_{A^\dagger A}(\omega)$$ and that to obtain such relation, you should just start off from... | The averaging here is a thermal trace:
$$S_{AA^\dagger}(t)= Tr[e^{-\beta H}A(t)A^\dagger(0)].$$
You need to permute it in order to change the order of the operators.
| {
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How can a photon collide with an electron? Whenever I study the photoelectric effect and the Compton effect, I have always had a question about how a photon can possibly collide with an electron given their unmeasureably small size. Every textbook I've read says that the photo-electrons are emitted because the photons ... | Let's start with a classical picture, where an electron possesses a negatively electric charges, $q=-e$, and light is an electro-magnetic field. Hence, in the classical description we expect that there exists an interaction between these two objects, because
*
*there exists an interaction between the electric field... | {
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Cross-sectional area of a Gaussian beam of particles On page 47 of the seventh edition of Particles and Nuclei, the authors write the following:
For a Gaussian distribution of the beam particles around the beam centre (with horizontal and vertical standard deviations $\sigma_x$ and $\sigma_y$ respectively), $A$ [the c... | I read your question again.
I can't say why a particle beam would have the same Gaussian beam shape as a laser. But in lasers, this is the most common and desirable beam. If nothing else, it has the most collimated beam because other modes have larger diffraction effects. Diffraction is often important for lasers.
Th... | {
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What's the meaning of a continuity equation with $\nabla^2 \rho$ on the right-hand side? I stumbled upon a continuity equation with a $\nabla^2$ term on the right-hand side:
$$ \partial_t \rho + \nabla (\vec b \rho) = D \nabla^2 \rho , $$
where $b$ denotes the forward velocity and $D$ is a constant.
What's the mean... | It is the so called convection–diffusion equation (but it is also known under other names). You may find more information in the above linked wikipedia page, but, in brief, it is an equation which combines a convective cause of time variation at one point (the $\nabla (\vec b \rho)$ term), with a diffusive process, co... | {
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Explicit form of a qubit state and relative phase In quantum computing, we can write our wave function as:
$$
|\psi\rangle=\alpha|0\rangle+\beta|1\rangle
$$
which can be rewritten as
$$
|\psi\rangle=\cos(\theta/2)|0\rangle+e^{i\phi}\sin(\theta/2)|1\rangle
$$
ignoring the global phase. This can be represented in a Bloch... | This is covered in very many textbooks. One example is the book of John Townsend. Anyways the point is if you write
$$
\vert\psi\rangle = \alpha \vert 0\rangle +\beta \vert 1\rangle
$$
you need $\vert\alpha\vert^2+\vert\beta\vert^2=1$ for normalization. Thus
$$
\alpha=e^{i a}\cos\frac{1}{2}\theta\, ,\qquad
\beta=e^... | {
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What is the meaning of a number changing process? On my lecturer's notes on Dark Matter I am told:
"It is customary to define densities normalised by the time dependent volume $V (t) = a(t)^3$. The reason for this is that, in the absence of number changing processes, the comoving number density remains constant with ti... | You are right. The number of particles does not change, but the volume increases as $V(t) = V_0 a^3(t)$, because of expansion.
Naively one can compute the number density as
$$
n(t) = \frac{N(t)}{V(t)}=\frac{N_0}{V_0 a^3(t)},
$$
where I used the fact that $N(t)=N_0$ in the absence of process that change the number of p... | {
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Calculating work of an object moving up a slope If an object is being pushed across a horizontal surface, the equation for the work done is $W = F s$, where $s$ is the horizontal displacement.
If an object is being lifted to a height of $h$, the equation for the work done is $W = F h$, where $h$ is the vertical displac... | It really depends on what forces exactly you are looking at. If it's friction & gravity, then total work done against them is :
$$ \begin{align}
W &= F_g h + F_{fr}~\ell \\
&= F_g h + F_{fr}~ \frac {h}{\sin \theta} \\
&= h \left( F_g + F_{fr}~ {\sin \theta}^{-1} \right)
\end{align}
$$
| {
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Does wave function always mean position in time? Does wave function always mean position in time? If we take an entangled state wave function $\frac1{\sqrt2} (|0>|0>+|1>|1>)$, we see nothing about position and time.
| A wavefunction $\psi(x,t)$ is the coefficient of a normalised vector in Hilbert space $\big(|\psi(t)\rangle\big)$ when expressed in the position basis $\big(|x\rangle\big)$. In other words,
$$|\psi(t)\rangle=\int dx|x\rangle\langle x|\psi(t)\rangle=\int dx|x \rangle\psi(x,t)$$
In your case, what you have is a vector in... | {
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How to write singlets and triplets in second quantization for fermions? It has been a long time I haven't done this and I am having a hard time writing things down in second quantization notation. Let us have a $n$-body system where the spin part and orbital parts are decoupled.
If want to write a two particle state, l... | The point is that the wavefunction is symmetric in spin for the triplet and antisymmetric for the singlet. So in your notation, the triplet is
$$\frac1{\sqrt2}(c^\dagger_{1\uparrow}c^\dagger_{2\downarrow} + c^\dagger_{1\downarrow}c^\dagger_{2\uparrow})|\emptyset\rangle$$
and the singlet is
$$\frac1{\sqrt2}(c^\dagger_{1... | {
"language": "en",
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How to compute expectation value $\langle e^{iH}\rangle$ for quadratic Hamiltonians? I have a rather basic, but actually non-trivial question:
We consider a bosonic system with creation operators $\hat{a}_i^\dagger$ and annihilation operators $\hat{a}_j$ and vacuum state $|0\rangle$ with $\hat{a}_i|0\rangle=0$. We cons... | Start diagonalizing H. You can follow this:
https://arxiv.org/pdf/0908.0787.pdf
Then use the power series of an exponential. You get the result in the diagonal basis. Make the inverse transformation and it is done.
| {
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Fraunhofer line width What sets the width of Fraunhofer lines on the solar spectrum ?
I first thought of Doppler broadening, but numerical applications result in much too high temperatures. For instance, using these data, I find a $\Delta \lambda =$ 0.01nm line width on the 630.25nm line of iron, corresponding to a te... | Your calculation sounds legit… Line profile looks similar in other high resolution data. I don't have any complete answer ; my guess would be unresolved Zeeman effect. It could be unresolved due to variation in B field over the field of view, even if the spectrometer itself is of high enough resolution.
Other reasons I... | {
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Is there any operator in quantum mechanics that measure an observable with non-zero uncertainty? What does a measurement do?
The answer is: If the detector is designed to measure some observable O, it will leave the measured object, at least for an instant, in a zero-uncertainty state.
I want to know, in the context of... | The uncertainty of an observable depends on the state $|\psi\rangle$ of the system that is being measured. The expectation value of the observable $A$ is given by
$$\langle A\rangle=\langle\psi|A|\psi\rangle$$
and the uncertainty is given by
$$(\Delta A)^2=\langle (A-\langle A\rangle)^2\rangle=\langle A^2\rangle-\langl... | {
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Why does the cosmological constant problem use the expectation value of the QFT vacuum energy? As I understand it, the famous 120 orders of magnitude discrepancy between the observed cosmological constant and the calculated QFT vacuum energy density relies on the vacuum Einstein field equations
$$G_{\mu\nu} + \Lambda g... | It is expected that a future theory of everything will solve this discrepancy which depends, as you observe , in mathematically comparing classical with quantum values .
At the moment the only theories that can quantize gravity and at the same time embed the standard model of particle physics, which is expressed in qu... | {
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Why do small animals appear to move faster than larger ones? I am keen to understand why smaller creatures move relatively faster than larger ones. Not only do they move faster, but their metabolism runs at a faster rate, they seem to process information faster (try swatting a fly!) - their entire lives seem to burn mo... | There are essentially two reasons. First, as they are smaller we are likely to look at them from nearer, creating the illusion of greater speed which results from greater angular speed subtended at the eye (just as when travelling by train or car, near objects cross our field of vision more quickly).
Second, they are l... | {
"language": "en",
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Why does frictional force depend on normal reaction and not the weight of a body? One possible explanation I came across for this was that if you have an external force and you press on the body, the body's frictional resistance to motion increases and hence it should depend on normal reaction and not weight.
| The two are same if the path is horizontal.
If the path is inclined/curved then it becomes necessary to distinguish between the two in the play out of friction in situations where we draw the force equilibrium diagram.
| {
"language": "en",
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Graphical explanation for length contraction I can understand the mathematical explanation for the reason why there should be a length contraction, but I fail to understand it intuitively. That is why I tried to explain it using spacetime diagrams, but for some reason, I was unable to do so.
Let us use the following ... | For an intuitive explanation you need a better diagram. The spacecraft measures length L at equal time in the spacecraft frame.
The spacecraft’s clock is in the bow. The spacecraft and Earth set their clocks to zero when the bow passes the Earth clock. Earth uses radar to measure the distance, $l$, from bow to stern, ... | {
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When Is It Appropriate To Use The Ladder Operator Method in Quantum Mechanics? I'm trying to understand when it is intuitively obvious that the ladder method would be best used to tackle a problem in quantum mechanics.
| Ladder operators might be one method of a solution if
*
*the system has a discrete set of eigenvalues of an observable operator (hamiltonian, angular momentum, etc)
*you can establish a non-zero commutator relationship between the ladder operators (usually an operator and its adjoint)
*the observable operator can ... | {
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Where did the work done by smaller force go? Suppose I have a spring of spring constant 150 N/m.One person pulls with it a force of 15 N. The extension produced is 0.1 m. Now another person comes and pulls with a force of 30 N (The first person is still there). The final extension is 0.3 m.The initial and final potenti... |
The work done by the bigger force is 6J which is exactly equal to the change in P.E of the spring.
Actually, this is incorrect. If we don't want to be adding kinetic energy and worrying about that, then the total force from the people must at all times equal the force from the spring. This means that the force from ... | {
"language": "en",
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Why are domains formed as separate units? I was reading about exchange coupling and domain formation in ferromagnetic materials. As far as I can understand, some of the dipoles in the ferromagnetic material align themselves in a group called a domain, and several such domains are formed with enough randomness to preven... | The interaction of atoms in a ferromagnet is typically modeled as an exchange interaction. The exchange interaction is related to the Pauli exclusion principle, which prohibits electron clouds of neighboring atoms from overlapping when the unpaired electron spins are aligned. This prohibition decreases the electrostati... | {
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Why are these quantization forms different? I'm confused about the form of the quantized electromagnetic field.
Sometimes, one writes the quantized electric field as
$$\hat E = \vec E_0(\hat a + \hat a^†)$$
, which can been seen the website below in the section, "Mathematical formulation 1".
https://en.wikipedia.org/wi... | The first expression, used in the Jaynes-Cummings model, is a description of the electric field at just one single point in space. This is useful when the region of interest (the size of an interacting atom or molecule, for instance) is small compared with the wavelength of the field; $E$ is nearly constant over this ... | {
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Which force makes the contact point of an object in rolling motion rise? When an object is rolling without slipping, the point at the bottom has no tangential velocity. When the point at the bottom rotates and rises, what force lets the point rise with tangential velocity from having no tangential velocity from before?... | In rolling motion it is not friction that is zero. Work done by friction is zero because all the points are just momentarily in contact with the rough surface.
Technically, as you said, the points are lifted up the next moment they come in contact with the floor. So, no displacement occurs in the direction of frictiona... | {
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Equation of state for ideal gas from Helmholtz free-energy Starting from the definition of Helmholtz free energy: $$F:=U-TS$$ (where $U$ is the internal energy , $T$ temperature and $S$ entropy) we derive in few steps the following relation: $$F=-T\int \frac{U}{T^2}\mathrm d T+ \text{constant} \tag{1}$$
Now, we know a... | In 1) there is additive "constant" of integration. The integration is only over $T$, the terms may depend also on volume $V$ which can be arbitrary. Therefore the "constant" in that integration over $T$ can be actually a function of $V$:
$$
F(T,V) = -T\int \frac{U}{T^2}dT + C(V)T.
$$
Since the first term, for an ideal ... | {
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In a vacuum, can you see light which is not travelling towards you?
In air, when there is light propagating in a direction, we can still see it even when it is not primarily travelling in our direction, because a small part of the light hits the air molecules, and changes its direction; it travels towards us.
Does thi... | In a universe that is shaped like the three-dimensional surface of a basketball whose space would be expanding at a rate initially almost exponential but eventually only quasi-inertial, like each of the local universes in at least one "bouncing" and inflationary cosmology (Nikodem J. Poplawski's "cosmology with torsion... | {
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QFT: 2d massless fermion propagator in coordinate space. Where am I wrong? I am trying to compute the fermion massless propagator in two dimension:
$i \int \frac{d^2k}{(2 \pi)^2} e^{ik \cdot x} \frac{k^0 \gamma^0 + k_1 \gamma^1}{k^2 + i \eta} = \frac{i}{(2 \pi^2)} \int dk^1 e^{ik^1x^1} \int dk^0 e^{-ik^0x^0} \frac{k^0 ... | From the $+i\eta$ in the denominator, I'm assuming you're using the $(1,-1)$ signature but then I'm not sure why you wrote $ik\cdot x=-ik^0x^0+ik^1x^1$. More importantly, your second mistake is in the claim of a pole at $k_1-i\eta$. The poles for the $k^0$ integration are at $\pm(|k^1|-i\eta)$, i.e. they involve the ma... | {
"language": "en",
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For a semiconductor, why does a band gap larger than the incident photon energy mean material transparency? If a photon with less energy than a band gap hits the band gap, why will the material be transparent? Although the photon cannot raise an electron in the conduction band to the valence band, why isn't the photon ... | The answer is contained in the question: in order to be absorbed the photon needs to raise an electron from the valence band to the conduction band.
Absorption here means transmitting the photon energy and momentum to the semiconductor. Being an electromagnetic wave, the photon is coupled to the charge in the semicondu... | {
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Why don't we use rapidity instead of velocity? In school we learn that we can add velocities together, and then later on we learn that it's not correct and that there is a speed limit. Why create all this confusion when we could just use rapidity to begin with?
Rapidity is defined as $w = \mathrm{arctanh}(v / c)$, wher... | As well as issues of practicality, it doesn't answer the question of why there's a speed limit. (It can't as it's just a mathematical transformation.). The question becomes 'in the formula for $w$, why do you take $c=3 \times 10^8$ m/s'?
| {
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If I apply a constant force to an object until I've reversed its starting velocity, does its final position remain unchanged?
A body of mass $m$ has initial velocity $v_0$ in the positive $x$-direction. It is acted on by a constant force $F$ for time $t$ until the velocity becomes zero; the force continues to act on t... | The total distance is a sum of two distances: $S_{1}$ and $S_{2}$, where the first is till the velocity goes to zero, the second: from zero to $-V_{0}$. $S_{1}=V_{0}t+\frac{1}{2}at^{2}$. Here $a=\frac{-V_{0}}{t}$. So $S_{1}=V_{0}t-\frac{V_{0}t}{2}=\frac{V_{0}t}{2}$.
The same for $S_{2}$ but with zero initial speed and ... | {
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Is the potential energy stored in a spring proportional to the displacement or the square of it? Suppose a mass of $M$ kg is hanging from a spring in earth. The mass will stretch the spring about $x$ m. So the change in the gravitational potential energy is $mgx$ J (supposing $x$ to be very small compared to the radius... | Note: The potential energy stored in a spring is proportional to the square of the displacement from equilibrium.
When you attach a mass to an unstretched spring, there will be a new equilibrium position for that mass on that now-stretched spring. About this new equilibrium position, you will have simple harmonic motio... | {
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How does cutting a spring increase spring constant? I know that on cutting a spring into n equal pieces, spring constant becomes n times.
But I have no idea why this happens.
Please clarify the reasons
| For a given deformation, the distance change between two adjacent particles (molecules/atoms) is more if you decrease the length of the spring. Thus, if you keep the displacement small enough so as the intermolecular force is linearly proportional to the intermolecular distance, the force required to produce the same d... | {
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Would a perfectly collimated laser beam have a flat intensity distribution? I'm trying to simulate a collimated laser beam in some FORTRAN and am wondering about the intensity distribution of a perfectly collimated beam: would it be a flat distribution (equal intensity across the beam) or it would be more of a gaussian... | "Top hat" optics can provide a nearly flat intensity distribution across a beam. A Gaussian beam is nearly flat near its center, so simply passing it through a circular aperture yields a nearly flat beam. A beam that is slightly nonuniform can be corrected by passing it through a customized gray-level filter to reduc... | {
"language": "en",
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Does the centre of charge behave as a point charge? We can find the centre of charge of a system of charges in much the same way we find the centre of mass of a system of masses
Suppose we have two charges of the same polarity and equal in magnitude that are placed at -x and +x along the x axis. The centre of charge wo... | No. For a simple intuitive example take a long rod containing a charge (uniformly distributed throughout its length). If you place a test charge a small one that does not adversely affect the charge configuration on rod, it will obviously suffer more attraction/repulsion from the elemental charge closer to it than fro... | {
"language": "en",
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What is the range of Pauli's exclusion principle？ In many introductions to the pauli's exclusion principle, it only said that two identical fermions cannot be in the same quantum state, but it seems that there is no explanation of the range of those two fermions. What is the scope of application of the principle of exc... | In principle it covers all Fermions in the Universe. Not two Fermions share the same quantum numbers. In a material with many moles of electrons each one of them has different values of energy level, etc. Of course, you have to consider, for example, that two electrons with the same n, l, m and spin numbers orbit two i... | {
"language": "en",
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Approximation from discrete Kronecker Delta to continuum Dirac Delta I am working on second quantization of the Dirac field with discrete momentum I was asked to compute the creation/annihilation anticommutator by imposing the anticommutators on $\psi$ i.e.
$$ \{\psi_a(\vec{x}),\psi^{\dagger}_b(\vec{y})\} = \delta^{(3)... |
Cited from Mahan's book. It may help you.
| {
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How to model a quantum circuit Let's say we have a system of 2 qubits, which are entangled in an unknown Bell basis configuration. Since the qubits are in a Bell configuration, each state is orthogonal to every other state, and thus must be distinguishable from each other.
My understanding is that there are 4 measureme... | Measurement is usually just defined as a gate on it's own. The "well known gate" that measurement maps to is simply the measurement gate. Its one of the few places where some difficult, hard to model interactions with an environment are allowed in a quantum circuit, so we just separate that part out.
For example, in th... | {
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Is 1 Joule the work done to lift ~100g through a distance of 1m? I am seeing many videos saying that 1 Joule is the work done to lift ~100g through a distance of 1m (like this one https://youtu.be/BYpZSdSEk4A?t=348).
The idea is that 100g has a gravitational force downward of 1 Newton. So lifting it means applying 1 Ne... | In your example of lifting an object, if the upward external force is exactly the same as the weight in magnitude, then the object is still in perfect equilibrium. And since the initial velocity of it was zero, its velocity would still remain zero because equilibrium means no acceleration. So, there would be no movemen... | {
"language": "en",
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Ideal gas temperature definition I have been doing some statistical mechanics and at the beginning of the course, I had seen this statement:
$$T^\circ (K) = 273.16\frac{\lim_{V\rightarrow \infty} (PV)_{\text{system}}}{\lim_{V\rightarrow \infty} (PV)_{\text{triple point of water}}}$$
Where, $T^{0}$ is the ideal gas temp... | The limit $V \to +\infty$ comes from the fact that for a given number of moles/gas particles, effects of interactions go down as the volume increases, because molecules are less and less likely to run into each other. This means that $\lim_{V \to \infty} (PV)$ can be deduced from the $PV$ of the equivalent ideal gas. B... | {
"language": "en",
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electrostatics- work done related question A point charge $q$ is at the center of an uncharged spherical conducting shell of inner radius $a$ and outer radius $b$. How much work would it take to move the charge out to infinity (through a tiny hole drilled in the shell)? I could not understand the question. Please help ... | You just need to find out the potential at the center of the shell. Work required to take the charge to infinity is simply negative of that potential assuming zero potential at infinity.
The shell is made of conductive material which means all the charge will accumulate at surface. If you imagine a spherical gaussian s... | {
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Why does the ideal gas law exactly match the van't Hoff law for osmotic pressure? The van't Hoff law for osmotic pressure $\Pi$ is
$$\Pi V=nRT$$
which looks similar to the ideal gas law
$$PV = nRT.$$
Why is this? Also, in biology textbooks, the van't Hoff law is usually instead written as
$$\Pi=CRT =\frac{NC_m RT}M$$
... | I'm answering your 2nd question:
It's a really easy proof :
You have $C_m=\frac{m}V$ and $C=\frac{n}V$ where $n=\frac{m}M$, thus $C=\frac{C_m}M$
Therefore :
$$\Pi=\frac{C_m R T}{M}$$
For $N$ the ions number it's related to biology, the ions are interacting and they cause this pressure, For example if it's $\mathrm{NaCl... | {
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Independent Elements of Elastic Stiffness and Compliance Tensor for ALL Space Groups In short: Does anybody know if there exists a compendium, a document, a book or a stone tablet listing the independent elements of the elastic stiffness and compliance tensors ( that is, naming the elements, e.g., $C_{1111},C_{2222},\l... | You might want to have a look at the figure at the bottom of:
https://serc.carleton.edu/NAGTWorkshops/mineralogy/mineral_physics/tensors.html
this also suggests that tetragonal cases can be split into two subgroups with slightly different symmetries.
| {
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Does a fan rotating with a uniform angular velocity consume electrical energy? Work done on a rotating body is equal to the change in its kinetic energy. When an electric fan rotates with a constant angular velocity, then its kinetic energy doesn't change. Does it mean that it doesn't consume electrical energy?
| As stated in the other answers, it is true that a fan rotating with a uniform angular velocity consumes electric energy due to the presence of energy dissipation. But it's not only due to the energy transferred to the air molecules (as others state as "air drag"), but also due to other factors like - friction in the be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/550239",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can the total momentum in the centre of mass frame be non-zero? I have a question regarding the usage of the centre-of-mass definition (which I thought required the total momentum, $p_T=0$) in the solution to the question given below:
A particular centre-of-mass energy is needed to create a new particle. We will do th... | The author explicitly states
We will do the calculation in a so-called fixed-target configuration.
So the calculation is done in what is usually called the laboratory frame, and calls it fixed-target in order to emphasize that the target is at rest in this frame.
Because of Lorenz transofrmations, any inertial frame ... | {
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Confusion about an example of inertia related to bus When the bus is stationary the passengers are also stationary. When the bus starts moving the part of the body (lower part) in contact with bus starts moving, but due to inertia the upper part remains stationary and thus he gets reclined back. If he is standing he wi... | The bus floor makes an horizontal force on the feet of the people. As the point of application of the force is at some distance from the centre of mass, there is a torque.
To an inertial frame outside the bus, people inside are not falling backwards, they are tilting, what is the consequence of a torque.
| {
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Are Dirac and Wu-Yang monopoles the same thing? When reading about the Wu-Yang monopole, it seems to me that the method that Wu & Young used (using patches and gauge transformations to cover $S^2$) is more systematic and general than Dirac's method for the Dirac monopole analysis (and for reaching the Dirac quantisatio... | *
*On one hand, Dirac-type and Wu-Yang-type magnetic monopoles usually refer to different mathematical descriptions of the same$^1$ underlying class of physical phenomenon in various space dimensions and with various gauge group:
*
*A Dirac-type monopole uses singular Dirac-strings/delta-distributions and globally... | {
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Why is electric flux through a cube the same as electric flux through a spherical shell? If a point charge $q$ is placed inside a cube (at the center), the electric flux comes out to be $q/\varepsilon_0$, which is same as that if the charge $q$ was placed at the center of a spherical shell.
The area vector for each inf... | From Gauss's law
$$\int\vec{E}.d\vec{s}=\frac{q_{in}}{\epsilon_{0}}$$
So the flux through both of the surfaces would be same as the charge inside both of the surfaces is same.
If we approach the problem through integral, you mislooked the angle between area vector and electric field in the case of cube.
| {
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Can we have pressure with zero net force on a 2d plane? From Wikipedia:
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Suppose we apply 2 equal and opposite forces on a 2d plane with area 'A' perpendicular to it ($F_a$ & $F_b = F$)
Will we ... | id you excert a force in one direction , you always have the opposite force it is called actio= reaction, otherwise , with only one force you accelerate your plane in the direction of the force.
as picture: you standing on the floor, exert a pressure of your weight divided by the area of your feet or shoes, but the ... | {
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Selections rules for spin what do we mean by the selection rule $\Delta S=0$?
Can you give me some example for hydrogen atom?
For example if I want to go from $1s$ to $2p$ how can I calculate $S$ for $1s$ or for $2p$?
| This question has already been asked in different forms. [Refer : 1) Selection rule ΔS=0: Why does a photon not interact with an electrons spin? 2) Does a photon interact with the spin of an electron?].
I will try to give you a summary of the very good points brought up. $\Delta S = 0$ actually is not a binding rule. B... | {
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Why is there an electric potential drop in electric circuits? I know a battery creates a potential difference, making an electric field that exerts a force on the electrons, who start moving. But why is there a potential drop after a resistor for example? How does it go in hand with electric potential being a scalar as... | The relations between currents, electric and magnetic fields in a circuit have to follow Maxwell equations. There is nothing there about resistances.
So it is possible to have a current in a closed circuit without any eletric field, (so no potential drop) since the relation between $\mathbf B$ and $\mathbf E$ are fulfi... | {
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Does This System Of Electric Charges Violate Conservation Of Energy? Imagine a system of 3 point charges and some kind of circular "rail".
All charges have the same magnitude - 2 are positive and one negative.
One positive charge is placed at some distance from the center of the circular rail.
The two other, are "glued... | In the bottom position, if there is some space between the two charges the positive charge at the bottom will push the positive charge away and attract the negative charge. This tends to push the two charges clockwise.
At the top the negative charge will be pulled towards fixed positive charge, while the positive char... | {
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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... | The answer is no, they are not the same things.
There is a tacit assumption when texts say things like "the average force," about what the average is performed over. Averaging over position is not the same as averaging over time.
You can always construct simple examples in which it just so happens that they are the sam... | {
"language": "en",
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How does focal length affect magnification? My answer would be the longer the focal length, higher the magnification will be, resulting in a larger image. But in a ray diagram, how does it look? I am searching for a comparison of ray diagram between short focal length and long focal length but didn't manage to get anyt... | If you are using the lens as a magnifying glass the standard formula $\frac{1}{u}-\frac{1}{v}=\frac{1}{f}$, where $u$ and $v$ are the distances from the lens to the object and image respectively and $f$ is the focal length, together with the formula $m=\frac{v}{u}$, show that in theory you can get any desired magnifica... | {
"language": "en",
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Acceleration in photoelectric effect In all the books I read, only the initial speed with which an electron is removed from a plate is mentioned, what happens to the acceleration?
Consider a plate (charge neutral and not connected to anything) and light of appropriate wavelength hits the plate
Suppose that an electron ... | After being ejected from the material, the electron is treated as a free particle, therefore acceleration is zero.
The metallic plate is macroscopic, namely it has $10^{23}$ and more electrons. Then, for all purposes, it remains neutral. If you want, you can think that it is connected to ground. Then, the hole which is... | {
"language": "en",
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De Broglie relationship What wavelength De Broglie relationship represents, if particle's motion is given by its group velocity (which is superposition of waves of many wavelengths)
| Assuming the electron is being modelled as a wavepacket, then there is no single momentum given by the de Broglie relation. We know this from the Heisenberg uncertainty principle:
$$
\Delta x \Delta p\geq\frac{\hbar}{2}
$$
Which tells that there is uncertainty in the position and the momentum of the wavepacket as can b... | {
"language": "en",
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What are some areas of physics, where the concept of "natural integral" may arise? Natural integral (as we will define it) is a distinguished antiderivative of a function that can be understood as interpolation of the sequence of consecutive derivatives to the $-1$. It has a naturally defined integration constant. Whil... | The natural antiderivative $$f^{(-1)}(x)~:=~\frac{1}{2}\int_{\mathbb{R}}\!\mathrm{d}x^{\prime} ~{\rm sgn}(x\!-\!x^{\prime})~f(x^{\prime})$$ is the most symmetric choice of integration constant. The kernel ${\rm sgn}(x\!-\!x^{\prime})$ appears all over physics. It is the Fourier transform of ${\rm PV}\frac{1}{k}$ up to... | {
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Since computer screens can't display many colors, where can I go to see the full color gamut? I found out recently that computer screens are only able to display a subset of all the colors visible to the human eye. Naturally one of my first questions was what do the other colors look like, but this is one of the few qu... | The colors you can see form (the positive orthant of) a three-dimensional real vector space. (A color is defined by three real numbers, describing the intensity of stimulation of the three types of cones.) A computer can display a finite number of colors. So you'll never get close to displaying the "entire gamut".
... | {
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Evaluating $\sigma^{\mu\nu}F_{\mu\nu}=i\alpha \cdot E+\Sigma\cdot B$ matrix, spin dependent term in quadratic Dirac equation I derive the quadratic form of Dirac equation as follows
$$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbra... | You did not quite explain how you failed to obtain the target result.
I would not like to spoil the fun of catching your factors and signs involved, so I will strictly deal with significant proportionalities.
$$ \sigma^{\mu\nu} F_{\mu \nu}= \sigma^{0i} F_{0 i}+\sigma^{i0} F_{i 0}+ \sigma^{ij} F_{ij}=2\sigma^{0i} F_{0 i... | {
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Intrinsic carrier concentration and bandgap My understanding is that the intrinsic carrier concentration of a wide bandgap material tends to be lower than that of a narrow bandgap material.
$$ n_i = \left(N_cN_v\right)^{1/2}e^{\left(\frac{-E_g}{2kT}\right)} $$
and the open circuit voltage of a solar cell is
$$ V_{OC} =... | The other terms in the equation for $n_i$ also matter. $N_c$ and $N_v$ depend on the effective mass. In particular, they are proportional to the effective mass to the three halves power. All things being equal, a higher band gap means a higher effective mass:**
This is something you can derive from k.p theory with a l... | {
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How do you measure the parity of a particle? When one looks up elementary particles on Wikipedia, as one of their properties their parity is stated. For example the Proton has parity $+1$, while a Pion has parity $-1$. I understand that you have to define the parity of some particles to have a reference to measure the... | If you look at the particle data group tables, mesons for example you will see for each resonance listed its parity, in the same line as the name and the mass of the resonance. Like the mass, it is an observation from measuring the resonance in experiments, laboriously in experiments over the years .
for example, the p... | {
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Do gravitational waves cause time dilation or not? There are a lot of questions on this site about gravitational waves and time dilation, and some of the answers are contradictory.
I have read this question:
Do gravitational waves cause time dilatation?
where Tom Andersen says:
In other words, if there was a beam of g... | I agree with G.Smith. A gravitational wave passing by causes distortions of space-time which means distortions of space and time. This distortion can be imagined as a gravitational potential well which inevitably involves time dilation. - Remember the Shapiro time delay. The only difference regarding curvature is that ... | {
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Is the zero-point energy of helium stronger than other liquids to disfavour freezing? Under normal atmospheric pressures, liquid helium does not freeze even when cooled very close to absolute zero. This is attributed to the uncertainty principle or due to zero-point energy.
But the quantum uncertainty or zero-point en... | For the sake of simplicity, I will answer the question for the bosonic species He(4). Although there are some subtleties for the Fermionic species He(3), due to the presence of total spin-$\frac{1}{2}$, the main message is the same.
The key points are summarized here as follows:
*
*The energy contribution from the... | {
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Simultaneity and special relativity Suppose, in inertial reference frame $F_1$, observers A and B are at rest, each having torch, and are separated by some distance and we have put machine M at middle of A and B.
Machine M has light bulbs on both sides ,right and left, so that if it catches light from A which is at lef... | A machine $M$ is not equidistant between $A$ and $B$ in $F_2$, so receiving their signals at the same time means they didn't send them at the same time, and they didn't. Totally self consistent.
| {
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Lorentz Transformation Proof - Special Relativity This is from A.P. French Special Relativity book, Chapter 3 (page 78)
Setup of the proof: $S$ and $S'$ be inertial reference frame. $S'$ move to the right with respect to $S$ at velocity $v$.
Let co-ordinates in $S$ be $(x,t)$ and co-ordinates in $S'$ be $(x',t')$
Equat... | Without loss of generality, let's assume $v$ is positive. From the viewpoint of the S' frame, the S frame is moving to the left with velocity $v$. (Equivalently, S moves to the right with velocity $-v$). Now, if we make a video of this, and play the video backwards, it will look like S is moving to the right with veloc... | {
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How is it physically possible that the electric field of some charge distributions does not attenuate with the distance? Let's consider for instance an infinite plane sheet of charge: you know that its E-field is vertical and its Absolute value is $\sigma / 2 \epsilon _0$, which is not dependent on the observer positio... | The answer is simple. It is not physically possible. No charge distribution can extend without limit. Every charge system is bounded. If you are farther away from a flat charge distribution than it's size, the electric field will attenuate with distance.
| {
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What causes neutrinos to be weakly coupled? When reading about "active-sterile mixing", which requires some Dirac mass ($m_D$) and some Majorana masses ($M_R$) to be very small but not zero, the seesaw limit model is discussed ($M_R \gg m_D$).
In this paper (Light Sterile Neutrinos: A White Paper), it is mentioned that... | There are two types of neutrinos there: active ones (part of the $SU(2)_L$ doublet, carrying the weak charge) and sterile ones (singlets of the SM).
The neutrinos mass matrix via the Dirac coupling mixes the two so that the active ones become a little sterile and the sterile ones become a little bit active (inherit som... | {
"language": "en",
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Why does adding a photon to the crystal of a semiconductor, gives a vertical transition in the reduced zone scheme? Why does adding a photon to the system, gives a vertical transition in the reduced zone scheme?
Considering me, it's due to the fact that a photon does not change de $k$-vector, is that correct? And why i... | A band structure is really a plot of energy versus momentum. Optical transitions are vertical in such a plot because the photon momentum can be neglected. The massless photon at the same kinetic energy has much less momentum than the massive electron, except in the ultra relativistic case.
| {
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Where is leverage calculated from in jointed system (car wishbone/spring rate vs wheel rate) Please let me know if this is on the right SE site.
In a car suspension, the spring typically acts partway along the wishbone:
As such, there's formulae for working out the leverage ratio that exists in the suspension. The met... | Leverage ratio
The leverage ratio $i_L$ is the relation between the spring deflection $d_S$ and
wheel deflection $d_W$ .
$$i_L=\frac{d_S}{d_W}$$
The leverage ratio is depending which wheel suspension you have and of the geometry of the wheel suspension.
Example: Mac Pherson strut
you start with the static equilibrium... | {
"language": "en",
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How do you combine two spatial modes of light into one spatial mode in optics? Is there a lossless way to combine light coming from two different single photon sources into one spatial mode? Either free space of fiber would be fine.
Let's assume the wavelength and polarization are the same in both input spatial modes.
... | No, two single photons coming from two different sources cannot be combined to form a superposition that represents one photon with one spatial mode. In other words,
$$ \text{two photon state} \neq |a\rangle + |b\rangle . $$
Even though the two photons come from different sources, they still give you a two-photon state... | {
"language": "en",
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Measurement of current and measurement of momentum of the electrons Is a measurement of the current flowing through some material a measurement of the momentum of the electrons? Does their wavefunction collapse to an (approximate?) wavefunction of momentum?
| Current is measure of average momentum(or velocity $v_d$) gained by the electron due to applied Electric field in a very short period of time($\tau$) between the collision with other electrons or ions in the lattice.
Since at room temperature the electrons are very frequently undergoing collisions, the electrons can de... | {
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How nerve signals preserve quantum coherence? Roger Penrose in this interview says he was trying to find out "... how it is that nerve signals could possibly preserve quantum coherence".
What does he mean by that?
| Penrose believes that the apparently non-deterministic nature of human thought and free will can be reconciled with the laws of physics if quantum uncertainty is somehow involved.
A colleague of his has developed the idea that the brain holds its long-term memory inside microtubule structures within the neurons (these ... | {
"language": "en",
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How does gravity smooth a planet? Over time, gravity (on a macro scale) and erosion (on a micro scale) will work together to smooth out a planet. How does the gravity work? Is it like erosion on a massive scale (ie pulling down the outside of a mountain) or does it un-deform the planet like unsqueezing a water ballon (... | For things the size of planets, gravity smooths them out through erosion and, to make things really smooth, wave action, underwater sedimentation, and tides.
For very dense objects like white dwarf and neutron stars and black holes, gravity is so overwhelmingly powerful that it smooths them out directly, without havin... | {
"language": "en",
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What will happen if I bring a positively charged body near the negative terminal of battery? Will the electrons flow from negative terminal of the battery to the charged body so as to neutralized a charged body..thus causing a decrease in pd of battery
| (a) I'll assume that the positive charged body is a conductor and that it is touched on to the negative terminal of the battery.
(b) Electrons will then flow from the negative battery terminal on to the body. The same amount of negative charge will be pumped through the battery from its positive terminal (and/or positi... | {
"language": "en",
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On particle diffraction and its relation to the statistical interpretation of the wave function Particles can be diffracted due to their quantum nature and that is understood by their wave-like behavior. Clearly seen in e.g. plane wave solutions of the Schrodinger equation or a superposition of states which can be seen... | In a section of Heisenberg's The Physical Principles of Quantum Theory; he emphasizes Duane's perspective on corpuscular picture of diffraction/reflection and points out for example for a grating, if it is known that the particle will hit a certain $$\Delta x $$ of the grating then the momentum will become uncertain by... | {
"language": "en",
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Why isnt the water from bottle dropping in the tub(volume of bottle/tub doesnt matter) until the level equalises? I can't seem to understand why water in the bottle wont drop down until the water level equalizes so pressure is same in any horizontal plane. As you can see just at tip of bottle,the pressure inside bottle... | The pressure in the bottle (at the top), Pi, is lower than the pressure outside: Po = Pi + Dgh.
| {
"language": "en",
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Can a fan cause a liquid to cool below room temperature? I enjoy the occasional hot drink, but place it below a small fan in order to cool it to a drinkable temperature. Unfortunately, as expected, I commonly forget about my drink, and it ends up very cold.
In fact, it ends up so cold that it feels much colder than I w... | As it's been asked about "fan", the fan can't cool anything by itself (imagine using a fan inside vacuum XD), it brings the fluid outside the container to motion hence helping to transfer the heat from container to the moving fluid(air in usual cases).
If we use much more cooler fluid we must be able bring down the tem... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/556234",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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D'Alembert derivation of Lagrange Equation - why can it use both virtual and normal differentials? In "Classical Mechanics" by Goldstein and "A Students Guide to Lagrangians and Hamiltonians" by Hamill I noticed that both the virtual displacement derivatives and the normal displacement derivatives are used at differen... | *
*On one hand, holonomic constraints and the Lagrangian itself are certainly allowed to have explicit time dependence, cf. e.g. the last term in OP's eq. (3).
*On the other hand, it's a well-established fact that the relevant (infinitesimal) displacements in the d'Alembert's principle and the principle of stationary... | {
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Evaluating sum of torques for different choices of origin when solving equilibrium problem My textbook says,
When applying equilibrium conditions for a rigid body, we are free to choose any point as the origin of the reference frame.
(source)
I am trying to understand this by looking at the following picture (from an... | The force of static friction is given by $$|\vec F_f| \le \mu_s |\vec N|$$ Since this is an inequality, you cannot use this to find the magnitude of friction, only whether $\mu_s$ is large enough to provide the necessary friction. Instead, the way to find static friction is based on the fact that it is static, i.e. not... | {
"language": "en",
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Does it actually take infinite (observer) time for someone to fall into a black hole? If you were to watch your friend approach a black hole, I understand that you'd see their clock slow until they appear frozen and redshift within a few seconds. But if you were to detect the increasingly long wavelengths coming off of... | It is not because of the doppler shift, but because of the gravitational time dilation. In the frame of an external stationary observer the infalling observer indeed never reaches the horizon.
If both observers carry entangled quantum bits, and the external observer makes a measurement on his first, he also determines... | {
"language": "en",
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Do virtual electron-positron pairs have mass? When a photon produces an electron-positron pair, do both these particles have mass? Why or why not?
|
Do virtual electron-positron pairs have mass?
Virtual particles are within an integral depicted by a Feynman diagram
Only lines entering or leaving the diagram represent observable particles. Here two electrons enter, exchange a photon, and then exit. The time and space axes are usually not indicated. The vertical ... | {
"language": "en",
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How do you hang a bottle off a toothpick? I came across this video: https://www.youtube.com/watch?v=mHsVxNMFWwA
How is this possible? I'm guessing the vertical toothpick is exerting an upward force on the table toothpick to balance the torque. But how? I am confus
| An easier way to understand why the arrangement is static is to think about energy. The arrangement will be static if it is in a minimum of energy. Addition of the two toothpicks to the rope/bottle arrangement introduces a geometric constraint that makes this arrangement a minimum of energy.
I don't know if you are fam... | {
"language": "en",
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How does RF communication between electronic circuit elements affect the circuit? The other day, a friend and I were looking at a simple resistor-capacitor-inductor circuit. As we were looking at the circuit, he mentioned that the capacitors and inductors "talked" to each other through the air. From this, I assume he m... | One form of this interaction which is real and has consequences is called radiated electromagnetic interference. This happens when the circuits are carrying high frequency signals, under which conditions a simple piece of wire in the circuit or a trace on a PC board becomes an antenna, broadcasting EM waves. When those... | {
"language": "en",
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Does energy conservation imply time invariance? This is similar to this question: Is the converse of Noether's first theorem true: Every conservation law has a symmetry?. However, the answer given there is very technical and general. I am only interested in the specific case of energy conservation (mostly because dark ... | You may possibly want this explained with regards to Noether's theorem or something similar, but the answer is yes if we're dealing with quantum mechanics. In quantum mechanics the time-translation operator is given as
\begin{equation}
\hat{T}(t) = \exp{(-i\hat{H}t/\hbar)}
\end{equation}
such that $T(t_{0})|\psi(t)\ran... | {
"language": "en",
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How do I get data of nuclear mass of each nuclide? I have been searching for a table of nuclear mass for a long time, but what I got are mostly data of atomic mass. The mass of electrons and the atomic binding energy might bring error to the calculation involving nuclear mass.
| You need a chart of the nuclides which you can access on line. There used to be posters of this but i don't know if its still sold. LiveChart has an interactive display and Wikipedia has a chart on their web site but it doesn't have your data included. The chart on Wikipedia is not complete but gives you an idea of how... | {
"language": "en",
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Are there any more physically representative analytical expression for a slit or edge than a step-function? What about ${\rm erf}(x)$ for example? Historically slits have been invaluable in teaching, research, and theory validation in both electromagnetic and quantum mechanics but conceptually they differ from what we ... | A reasonable mathematical model for a gradual transition from one state to another is the $\tanh$ function.
Thus
$$ T(x) =\frac{1}{2}\left( 1 + \tanh(x/t)\right)$$
smoothly transitions from $T=0$ when $x<0$ to $T=1$ for $x>0$, with a characteristic "width" for the transition of $\pm t$ about $T=0.5$ at $x=0$. A sharp e... | {
"language": "en",
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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?
| Short answer is that it boils, but it boils differently because it's either evaporation from a liquid surface in low temperature or "bulk evaporation" aka. boiling, due to temperature gradient. Now because oven heats more or less uniformly all sides of pot is heated the same, thus eliminating clear temperature gradient... | {
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Expansion Postulate Quantum Mechanics How does the expansion postulate allow predictions to be made about measurement outcomes?
I understand the postulate as:
$$
ψ =\sum_{n} a_n φ_n
$$
with coefficients calculated by:
$$
a_n =\int φ_n^*ψdτ.
$$
I think that:
$$
|a_n|^2
$$
is the probability of the system being in state... | The postulates of quantum mechanics say the following about measurements. Consider a physical quantity represented by an operator $\hat{O}$, whose eigenvalue equation is $\hat{O}\phi_n=\lambda_n\phi_n$, for eigenvalues $\lambda_n$ and eigenstates $\phi_n$. The outcome of a measurement of this physical quantity is then ... | {
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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, ... | Whether you feel a shock depends on how much current flows through your hand. How much current flows through your hand depends on the resistance along the whole path of the circuit, not just in your hand.
For example, if you put a battery on a table and then put a resistor a few inches away from the battery, there woul... | {
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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 layman's terms, something is “almost infinite” if it is so large that
it would make no difference if it was any larger. This can be formalized
with the mathematical notion of limit, as shown in previous answers.
Here, I would just like to add a simple illustration. Here is a picture
of my 35 mm lens:
See the infini... | {
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Continuity equation in QM I found this question in a quantum mechanics exam:
What is the physical interpretation of the continuity equation $\frac{\partial\rho}{\partial t}+\frac{\partial j}{\partial x}=0$? Here $\rho(x,t)$ is the probability density and $j(x,t)$ is the probability current.
I assume they want a one lin... | The continuity equation in 3-dimensions is
$$\frac{\partial \rho}{\partial t} + \vec{\nabla}·\vec{j}=0$$
where the second term is the divergence of $\vec{j}$. By integrating this equation within a fixed volume $V$ whose boundary is $\partial V$, and applying the divergence theorem, we get the integral form of the conti... | {
"language": "en",
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Symmetry factor of certain 1-loop diagrams in $\phi^4$-theory I have to derive a formula for the symmetry factor of the diagrams of the form
in $\phi^4$-theory, where $\phi$ is a real scalar field. By symmetry factor I mean only the number of possible contractions, which lead to the same diagram (without the factor $1... | OP's exercise seems to conflate the number $n$ of external legs and the number $m=\frac{n}{2}$ of 4-vertices. The symmetry of an $m$-gon is $S(m\text{-gon})=2m=n$. The symmetry factor of the relevant 1-loop Feynman diagram is then $S=2^m S(m\text{-gon})=2^mn.$ For each vertex, there is $\begin{pmatrix}4\cr 2 \end{pmatr... | {
"language": "en",
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Understanding quantum cross sections as areas In scattering cross sections we deal with $d\sigma/d\Omega$, incident area per scattered solid angle. When a particle scatters into a small finite $\Delta\Omega$, the incident particle was in a small finite area $\Delta\sigma$. However, in QM the incident state is a plane w... | Here's my take on the thing, based on what is expressed in chapter 11 of N. Zettili's Quantum mechanics: Concepts and applications. The scattering cross section is defined as the number of particles $d\sigma$ scattered into an element of solid angle $d\Omega$ defined by the angles $(\theta, \varphi)$. This is related w... | {
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Intuition of sound wave impedance and admitance The impedance of a soundwave is given by both:
$$\frac{\mathcal{P}}{V}=\rho_0c$$
Where $\mathcal{P}$ is the pressure wave, $V$ is the velocity vector of particles, $\rho_0$ is the static value of the gas density and $c$ is the speed of sound\wave.
It is very easy for me t... | Impedances in circuits are extrinsic while in your questions you are showing the intrinsic acoustic impedance. As you pointed out, it is a material property and intuitively you can say that it shows you how easy it is for a given pressure to obtain a particular particle velocity. I suggest that you check my previous a... | {
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Dispersion Relation of Quasiparticle in Superfluid I am now reading a book "Superconductivity, Superfluids, and Condensates" by Jame F. Annett. I am stuck at the part of writing dispersion relation of the quasiparticle in superfluid here. The author does not seem to give any explanation about this. He somehow mentioned... |
According to the dispersion relation above, which was obtained by neutron scattering, we can see firstly see that the quasiparticle has the linear dispersion relation at low energy.
Imagine now we drap an object of mass $M$ in the fluid (that object can be a defect at the tube wall), the momentum of the object is init... | {
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Why is a projectile trajectory parabolic while that of a satellite elliptic? I understand that the parabolic trajectory is an approximation of a more elliptical trajectory, since acceleration due to gravity is taken to be a constant for a projectile. However I'm intrigued to know that what changes in kinetic and potent... | We consider the mechanical energy of the object in orbit due to a central force to be
$$E=\frac{1}{2}mv^2 + U(r)$$
where $m$ is the reduced mass of the object, $v$ is the instantaneous speed, and $U(r)$ is the instantaneous potential energy of the system due to the central force.
There are three general values for the ... | {
"language": "en",
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Why does the energy of an electron inrease with its shell number inside an atom? According to this:
$ E = \frac{-13.6 Z^2}{n^2} $
the energy of an electron is, well, higher the farer it is away from the core. I found this confusing as I need to put less energy to release an electron when it is on the 5th shell than whe... |
Why did they do that? Why is a minus better than a plus?
Firstly, understand that when the electron is 'infinitely' far from the nucleus its energy is $0$ (assuming it is also stationary).
But empirically we also know that when an electron 'falls' from a higher orbital ($n=n_1$) to a lower one ($n=n_2$ where $n_2<n_1... | {
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Ideal wire and resistance I am having a bit of trouble understanding what an ideal wire is.
Let's assume there is a positive charge on the positive terminal of the battery and a negative on the other side which will give us the same results. Now electric potential is given as integral of E.dr. Therefore the potential w... | If you short an ideal voltage source (V) with an ideal wire (R=0) then an infinite current I will flow such that V=IR . In practice a fire or explosion will result to remind you that idealisations are approximations to reality.
| {
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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... | In order to observe an electron one must interact with it in some way. For example one could shine light at it so that it scattered the light, or one could arrange for it to hit something like a multi-channel array (a charge detector with many small elements). The various observers will study some sort of large-scale s... | {
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Why isn't the work done by gravity positive in this situation? I want to find the work done by the force of gravity to move an object of mass $m$ from infinity to a point $P$ at distance $r_p$ from a body of mass $M$ (that I assume fixed). The formula should be
\begin{equation*}
W = \int_{\infty}^{P} \vec{F}(r) \cdot d... | $\begin{equation*}
W = \int_{\infty}^{P} \vec{F}(r) \cdot d\vec{r}
\end{equation*}$
$\vec r = r \,\hat r$ is the displacement from the centre of the mass $M$ and $d\vec r=dr\,\hat r$ is incremental displacement.
The gravitational force is attractive and so in the opposite direction to $\hat r$ thus $\vec F(r) = -G \dfr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
in photoelectric effect, where do electrons go when they are ejected from metal? When light shines on a metal, electrons are ejected from the surface of the metal provided the energy of the photons are greater than the work function of the metal.
My question is:
*
*Where do the ejected electrons go? Are they running ... | the electrons are actually ejected from the surface of the metal. If the metal is surrounded by a vacuum, the electrons form a cloud close by called a space charge. If there is a positively-charged piece of metal close by, the loose electrons are attracted to it and their flow is called a photoelectric current.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/560645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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