Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Ramsauer-Townsend effect one dimension I am trying to learn basic one dimensional quantum mechanical scattering. The approach used is studying the stationary wave with a square potential barrier with $V_0$ as the positive potential and $L$ as the length of the barrier.
My textbook says that for certain energies, namely... | I found my answer. What I did wrong when drawing my picture was to make a phase shift at both boundaries of the square potential. There is supposed to only be a phase shift at one of the boundaries. This is analog to an electromagnetic wave where phase shift or not is dependent on whether the electric permitivity is in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/314179",
"timestamp": "2023-03-29T00:00:00",
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Effective potential of radial equation of Hydrogen In QM, the study of the hydrogen atom, why does it follow that for the radial equation given as $$-\frac{\hbar^2}{2m}\frac{d^2 u}{d r^2} + \bigg( -\frac{e^2}{4 \pi \epsilon_0} \frac{1}{r} + \frac{\hbar^2}{2m}\frac{l(l+1)}{r^2} \bigg)u = Eu,$$ the term $\frac{\hbar^2}{2... | The term
$$V_\mathrm{centripetal}=\frac{\hbar^2}{2m}\frac{l(l+1)}{r^2}$$
is an effective potential because it appears in the radial equation in the same way (coefficient of $u$) as the Coulomb potential
$$V_\mathrm{Coulomb}=-\frac{e^2}{4\pi\epsilon_0r}$$
The Coulomb potential is attractive for opposite charges which yo... | {
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"url": "https://physics.stackexchange.com/questions/314432",
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Real images and their formation We're told that a real image is formed when light rays actually converge to a point. That's all good. But what happens if a screen isn't there to take the image on? Is it still there?
| Please note that my answer is totally in the framework of geometrical optics.
The point where the real image is formed is where rays converge. After this point, rays will naturally diverge, as if they were coming from a point source of spherical waves. You can see an example of this phenomenon here.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/314519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In thermodynamics what is a constant mass process called? In thermodynamic processes you'll see defined conditions like isochoric for constant volume and isothermal for constant temperature, as examples.
In a general thermodynamic process you may have a flux of mass across the control volume, but in many cases the mass... | It's simply a closed system
In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings. An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/314618",
"timestamp": "2023-03-29T00:00:00",
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Looking for a good casual book on quantum physics I'm looking for something that is going to blow my mind without any scientistic ideas (e.g. something that sounds like science, but doesn't have anything in common with science), written by a professional physicist who spent a lot of time considering "what it all means... | I really enjoyed
*
*Quantum: a guide for the perplexed, by Jim Al-Khalili
though to be honest it's now getting uncomfortably close to fifteen years since I read it as a high school student, and I don't have my copy at hand to give it a critical assessment. As a high schooler I found it engaging and accessible, a... | {
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What does one second after big bang mean? Consider the following statement:
Hadron Epoch, from $10^{-6}$ seconds to $1$ second: The temperature of the
universe cools to about a trillion degrees, cool enough to allow
quarks to combine to form hadrons (like protons and neutrons).
What does it mean to say "from $10^... | We know that time passes differently for different observers, and the question is how can a time be given without telling which frame it is in. The answer is that there's a preferred reference frame in cosmology, the comoving frame, because of the fact that there's matter and radiation in it.
Intuitively, the special f... | {
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Method of image charges for a point charge and a non-grounded conducting plane I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane isn't grounded, or is connected to a poten... | The problem is addressed in Electrodynamics Fulvio Melia Example 2.1 page 39,
using Green function techniques. However, I cannot fully understand his final
solution. Let us define the plane held at a constant potential $V_0$ to be the $z$-$y$ plane. The charge $q$ is at the distance $a$, namely at $(a,0,0)$. The potent... | {
"language": "en",
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Does entropy depend on the observer? Entropy as it is explained on this site is a Lorentz invariant. But, we can define it as a measure of information hidden from an observer in a physical system.
In that sense, is entropy a relative quantity depending on the computation, measurement and storage capacity of the observe... | I think that Shannon-von Neumann definition of Entropy pass this anthropocentric paradox by establishing the minimum amount of information that cannot be reversibly be exchanged between two states of the same system, no matter if there is an agreement or even the presence of observers. In such way Entropy is indeed a p... | {
"language": "en",
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Why is it possible to use free energy functions on Boltzmann factor? When the Boltzmann factor is derived on the canonical ensemble, one gets the exponential function of the energy:
$\large{e^{-\frac{E}{k_b T}}}$
However, some texts (it is very common on physical-chemistry, for exemple) just assume that you may use Gib... | I am new to this, so if I am missing something obvious, my apologies. Also, I have not dealt with TD from the chemical or biology perspective.
Assume a given energy, $e^{-E/k_BT}$, provides the relative probability of a particular microstate. Now assume that we are concerned with a isobaric system, so E goes to H, (the... | {
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Would a gas "weigh" less than a liquid if they have the same mass? Thought experiment: I acquired two boxes of the same dimensions and same weight. One box contains $1\ \mathrm{kg}$ of water at room temperature while the other box has $1\ \mathrm{kg}$ of water, but in steam form, because the temperature of the box is a... | Skip the difference between mass and force. They both experience the same gravity.
Yes a liter of water is 1 kg
A liter of steam is about 1/1000 of that or about 1 g. More precisely 1.67 g (at 100C and 1 atm).
If you mean put 1 L of water in a 1 L box and heat it to 100C or even 200C then it will also be 1 kg.... | {
"language": "en",
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Conceptually, why is acceleration due to gravity always negative? As the title states, why is acceleration due to gravity always (-). Say you assign "up" as the positive direction. If an projectile is thrown at a 24 degree angle above the horizontal, I get that acceleration due to gravity before the vertex is negative.... | I don't have enough reputation to make a comment, so I'm adding this as a separate answer.
The other answers are not wrong, but I feel it is worth pointing out that this is related to the fact that, as far we know, there is only type of gravitational charge (i.e. mass), which we by convention call positive. If I recall... | {
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Can there be really a theory of everything? If quantum theory becomes compatible with Einstein's theory of gravity, we get the theory of everything. But if it can predict anything in the universe (provided boundary equations are given) wouldn't it predict itself. I mean won't the theory tell us when the theory will be ... | Your question seems to stipulate that a Theory of Everything must be self-reflexive. In other words, that it allow a "consciousness" of itself, or that it explain itself. Don't all workable theories do this?
Alternatively, your question may suggest that a Theory of Everything must predict the time at which it will b... | {
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Why do we invent non-physical concepts (like e.g. point particles) to study physical phenomenons? There is nothing exist like point particles in reality then why did we invented the notion of point particles and how does it relate to real world?
|
then why did we invented the notion of point particles
Because that makes it simpler to work with.
*
*Sometimes we say "it costs 24 \$" even though it is actually 23.99 \$.
*We also usually say that there are 365 days on a year, even though there actually are $\sim$365.24.
We are accepting a tiny error margin, ... | {
"language": "en",
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How to handle a Dirac delta at $r = 0$ for a first Born approximation? I have been trying to get my hands around a scattering problem all day but I can't wrap my head around the idea. It's a scattering problem with First Born Approximation and the potential is a Dirac delta sitting at the origin. The standard procedure... | The general formula for the first-order approximation of $f(\kappa)$ is
$$
f(\kappa)=-\frac{m}{2\pi}\int\mathrm d\boldsymbol r\ \mathrm e^{-i\boldsymbol\kappa\cdot\boldsymbol r} V(\boldsymbol r)\tag{A}
$$
In the particular case
$$
V(\boldsymbol r)=a\delta(\boldsymbol r)
$$
we have
$$
f(\kappa)\overset{(\mathrm A)}=-\fr... | {
"language": "en",
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Why do we not feel weightless at equator but feel in satellite A person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. My question is, why does he/she not feel weightless as a satellite passenger does?
If we compare a geostationary satellite with the earth's equa... | You do weigh slightly less at the equator than on the poles. however escape velocity is much greater than rotational velocity.
| {
"language": "en",
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Volume of hypothetical closed universe Consider a physical universe with a beginning in time and space, with a finite amount of mass without the complications of dark energy that we have in the presently open curvature universe, so that the omegas (vacuum and mass) values create a closed universe, a universe with posit... | The radius of curvature is
$$\rm r=\frac{c}{H \sqrt{\Omega_t-1}}$$
where $\rm H$ is the Hubble parameter and $\rm \Omega_t$ the sum of all energy contributions:
$$\rm \Omega_t=\Omega_r+\Omega_m+\Omega_{\lambda}$$
so the circumference where a straight line closes in on itself is
$$\rm U=2 \pi r$$
The volume of the 3dime... | {
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Will fracture occur under very high hydrostatic pressure? In the case of tensile loading, the distances between atoms or molecules increase and finally the material is broken because of bonds breakage between atoms or molecules. But, what about the hydrostatic loading? Will the atomic bonds break when they close to eac... | In the context of everyday forces and pressures (i.e., no neutron stars or black holes), consensus is that homogeneous (non-porous) materials can withstand arbitrarily high hydrostatic pressure without failure (although other transformations not involving fracture, such as a phase change, might of course occur). In ot... | {
"language": "en",
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How can I solve the moment of inertia?
The source tells me to use the formula for a ring, but it is not possible, as the portions are nearer to the axis than a normal ring. How can I find the moment of inertia?
| You know that to solve this problem you will have to use the integral form for MoI.
$\int_0^Mr^2dm$ where $dm$ is the mass element (geometry of the problem) and $r$ is the distance from the axis of rotation.
You express the mass element in terms of $r$ so you get linear density.
Ex. Rod of mass $M$ has linear density $... | {
"language": "en",
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Falling spool acceleration explanation In this example both spools A and B have the same downward acceleration. Why would the net downward force on Spool A be the same as for Spool B despite having more total kinetic energy?
| The net vertical force on the spools is the same because the tension upward is the same for both, and the weight downward is the same for both.
This is consistent with the difference in the kinetic energy because, the work done by gravity is the same for both, but the work done by the tension is not the same for both.
| {
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What determines the direction of a path on a line integral (vector case)? Line integrals are very important to use in Physics. For example, we calculate work by: W=∫<F,dr>. But I just got confused about something. What determines the direction of motion? The integral limits, or the vector dr?
Well, when we do the inter... | *
*The line segments $\mathrm d\vec r$ determine - define - the exact path.
*The integral itself decides - via the order of its limits - the direction along this path. Meaning, flipping around the integral will only change the sign of the integration.
Both are thus involved with determining the path direction, but t... | {
"language": "en",
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Why do ice cubes shrink in the freezer? OK before you all yell "EVAPORATION", I know that's the boilerplate answer, but why and how.
Back in high school we were taught water, and most other elements and compounds, have three states, solid, liquid, and gas. Which state it's in being dependent on temperature and pressure... | I had never really noticed that happening, so before I said "that seems odd, are you sure?" I did some research and surprised myself.
According to the Wikipedia page on freezer burn water will sublimate from the surface of ice if the air temperature is low enough and the air is dry enough.
The reduced vapour pressure o... | {
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Where are the poles of the wire? When current is passed through a copper wire there are circular magnetic field lines around it but where are the north and south poles to that circular magnetic field?
| The poles of a magnetic field, like the pot of gold said to be at the end
of the rainbow, can be found by following along the field-line path. So, if you point
at the magnetic North pole on Earth, and follow that path, you go ... North.
If you examine that field line, however, you'll soon note that it ISN'T
pointing ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/317667",
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How does voltage affect boiling ability of a kettle? I was reading an article about the lack of electric kettles in the USA - the claim at the end states one reason is the lower voltage at the socket. Personally, I think that the main reason is that morning tea is not as big in the US as it is in the UK or Australia, b... | For a fixed voltage $V$ the power dissipated by the element in the kettle is $\frac{V^2}{R}$. To increase the power so that the water boils as fast in the USA as it does in the UK, you would need to reduce the resistance of the element. Alternatively, you just use the same kettle as in the UK and wait longer.
The domes... | {
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How Do I Increase The Range Of An Home Made Electromagnet? Please forgive me, I am new to this forum and I am not a physics guy but any help would be appreciated. I would like to know how to I increase the range or reach of my electromagnet. By range, I mean the distance from my magnet to a metal object (paper Clip). C... | There are three main ways to improve your electromagnet without needing a physics degree to model the magnet.
1) Put more current through the magnet. You will need a higher voltage power supply to do this.
2) More loops of wire. This one is a bit tricky since the increased length also increases the resistance, so if yo... | {
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Generalized forces in Richard Fitzpatrick's Newtonian Dynamics In Richard Fitzpatrick's Newtonian Dynamics, page 128, generalized forces are defined as
\begin{equation} \tag{9.6}
Q_i = \sum_{j=1}^{\mathcal{F}} f_j \cdot \frac{\partial x_j}{\partial q_i}.
\end{equation}
Here, $q_i$ are generalized coordinates, $x_j$ a... | $$Q_i = \sum_{j=1}^{\mathcal{F}} f_j \cdot \frac{\partial x_j}{\partial q_i}$$
$$\implies Q_i = -\sum_{j=1}^{\mathcal{F}} \frac{\partial U}{\partial x_j} \cdot \frac{\partial x_j}{\partial q_i}$$
$$\implies Q_i = -\sum_{j=1}^{\mathcal{F}} \frac{\partial U}{\partial x_j} \cdot \frac{\partial x_j}{\partial q_i}$$
$$\impl... | {
"language": "en",
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Finding the symmetry of electron spin and position states using Clebsch-Gordan tables? I know that spin and position states must be symmetric and antisymmetric (and vice versa), but I can't figure out how to use Clebsch-Gordan Tables to figure out the symmetry of either one.
For example, Carbon's ground state has a tot... | Carbon has two valence electrons in the p-shell. To obtain total spin $S=1$ the spin wavefunction must be symmetric. The best way to see this is that the $S=1$ states will contain a $M_s=1$, which must be unique product $\vert 1/2,+\rangle_1\vert 1/2,+\rangle_2$, clearly symmetric under permutation.
As a result, the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/318351",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Derivation of the electric dipole radiation An harmonic oscillating source will emit fields of the form
\begin{align}
&\mathbf{H}=\frac{ck^2}{4\pi}(\mathbf{n}\times\mathbf{p})\frac{e^{ikr}}{r}\left( 1-\frac{1}{ikr} \right) \tag{1}\\
&\mathbf{E}=\frac{1}{4\pi\varepsilon_0}\left\{ k^2(\mathbf{n}\times\mathbf{p})\times\ma... | Note that $\mathbf{n}$ is not a constant vector but dependent on position. You have not taken the derivative of this, which is the source of error.
In particular, you say
$$\nabla \times (f\mathbf{v}\times\mathbf{w}) = \nabla f \times (\mathbf{v}\times\mathbf{w}).$$
This is incorrect, the correct expression would be
$$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Expressing position due to gravitational acceleration as a 3-Dimensional differential equation I know that the force of gravity is $F = \dfrac{G m_1 m_2}{r^2}$. Now assume in a one-dimensional system there are two masses in the universe, a planet and an object. The object would have an acceleration of $A = \dfrac{G ... |
My question is now how to transform this to 2 (and 3) dimensions
I am not sure where your problem is in doing this. In 3 dimensions using
$$\mathbf{x}_1 = \begin{pmatrix}x_1\\y_1\\z_1\end{pmatrix}, \mathbf{x}_2 = \begin{pmatrix}x_2\\y_2\\z_2\end{pmatrix}$$
to denote the position of $m_1$ and $m_2$ respectively, the e... | {
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Why doesn't saturation current in the photoelectric effect depend on the frequency of light absorbed by the metal emitter? If current $I$ is given by $I = nAev$, where $n$ is the number of electrons per unit volume, $A$ is the area, $e$ is the charge of an electron and $v$ is the velocity of the electron, it must mean ... | In photoelectric effect the electrons will eject when sufficient frequency of light is incident. The saturation current will depends on the no.of photoelectrons ejected per second.As the frequency increases the energy in the quantum packets increases but the no. Of photons that should incident on the cathode plate rem... | {
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Normal order of 1 Say in my Hamiltonian I had a term
$$Q[a_j,a^\dagger_j]_\pm$$
where $Q$ is a constant. Suppose I didn't realise that this quantity equals 1 and calculated a normal order. Of course you get 0
However, the normal order of 1 should be 1 or else any operator could be multiplied by 1s and get 0 at the end.... | Well, it depends on context. E.g.:
*
*Assume we are given a classical model that we want to quantize, i.e. to construct a corresponding quantum theory. Be aware that quantization is not unique. The classical theory doesn't know about operator ordering so this introduce ambiguity. To parametrize our ignorance we shou... | {
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Measuring Vibration I want to measure the vibration in an environment so that I can isolate some equipment. What is the standard way of measuring this? Basically, I want to mitigate the effects of a nearby train. More important than the loud horn, I need to isolate the equipment from vibrations in the ground. I am look... | There is no need to measure the vibration. The unwanted vibrations must be having some undesirable but detectable effect on the output of your experiment. The effect you are getting compared with what you expect from ideal conditions is a measure of the noise. The improvement in your output signal will tell you what ef... | {
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How is entropy a state function? Is there only one reversible way to move from one state to another?
If we consider two states $A$ and $B$ on an isotherm and we move from $A$ to $B$ by first reversible isochoric process and then reversible isobaric process. Now the path followed should be reversible since both the ... | The total heat added in both the processes is different. Change in entropy is defined as $\int(dQ/T)$. Along the isotherm, the temperature remains constant. But along the other two reversible processes you have mentioned, the temperature is not constant. Effectively, it can be seen by integration that change in entropy... | {
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Why does rainwater form moving waves on the ground? Is there a name for this effect? A while ago it was raining and I noticed that, on sloped pavement, water was flowing in very regular consistent periodic waves, as you see below.
However, I realized I had no idea why this should be happening. There was nothing uphill ... | I may have an explanation. Such a behavior is not to be expected (perhaps) in an ideal situation (uniform surfaces etc.). So, if it's due to an irregularity, the following may be true.
Suppose that we have a small bump/irregularity/cavity on the road (very small, perhaps a cm in height, and a bit longer along the road)... | {
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Electric field lines: and nature in presence of a conductor Long cylindrical shell carries positive surface charge σσ in the upper half and negative surface charge −σ−σ in the lower half. The electric field lines around the cylinder will look like figure given in: (figure are schematic and not drawn to scale)
Note: n... | The problem is the discontinuity in your field lines, as you suggest. Unless the electric field goes across a charged surface it should be continuous and its derivative should also be continuous. Basically the field lines must be smooth unless there is charge near that field line.
I'm not sure how much calculus you ... | {
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Can a Lagrangian be such that all possible paths have the same action? Q: Can a Lagrangian be such that all possible paths have the same action?
I was thinking if a Lagrangian of the motion of a particle could be represented as the total time derivative of some arbitrary function. In that case the action $S=\int^A_B L ... | Well, mathematically, you've worked it out.
Typically, theories like these are called Topological field theories, since the action depends only on the dyanmics at the boundary. It is a field unto itself, but note that a lot of the typical reasoning you see in, say, Goldstein doesn't really work, because the equations ... | {
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Photoelectric effect:- Reduction of wavelength increases current? I did a question in which, the intensity of the incident radiation on a metal surface was kept constant but the wavelength of the photons has been reduced. The question inquired what will be the effect on the maximum photoelectric current? The initial wa... | It is the interface between classical electrodynamics and quantum mechanics.
Intensity is a classical electromagnetic wave measure of energy, measured by the average electric field in the wave :
the average intensity for a plane wave can be written
So for a given value of intensity/energy for a classical wave of f... | {
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How do I get the position at time $t$, if acceleration depends on position? In my visit to more realistic particle motion animation, $F=\frac{kq_1q_2}{d^2}$, $F=ma$, so: $$a=\frac{kq_1q_2}{md^2}$$ My velocity, integrating the above (from a site because I forgot how to do it), is $v=-kq_1q_2md+v_0$. Curiously, the integ... | $$a = \frac{dv}{dt}$$
$$a = \frac{dv}{dt} \frac{dx}{dx}$$
$$a = \frac{dv}{dx} \frac{dx}{dt}$$
$$a = v\frac{dv}{dx}$$
$$\int_{x_0}^x a.dx = \int_{v_0}^{v} v. dv$$
Here, $x$ is not the final position; it is a variable. Note that we are solving the differential equation for a general case.
$$2\int_{x_0}^x a .dx = v^2 - v^... | {
"language": "en",
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Why does a plastic comb attracts tiny bits of paper if it is an insulator? When we rub plastic comb against dry hair, it attracts tiny bits of paper. We know that plastic comb is an insulator of electricity but then how is it getting charged and showing the property of attracting?
| because of electrostatic forces acting on it.
when we rub the plastic comb it will either be charged negatively or positively.
it will induce negative charges on the bits of paper if the comb is positively charged so, the bits of paper will be attracted by the plastic comb which is an insulator
| {
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Real reason behind why current splits in a parallel circuit Is it true that the speed of electrons in the branches is smaller than in the main wire as the current splits in a parallel circuit? If its true, how does the speed reduce (the mechanism, not because of the laws alone)? If not, then what really causes the smal... | The answer depends on the wires in the branches and the main wire are made out of and what shapes they have. What you can know for sure is that the sum of currents in the branches is the current in the main wire.
Now the current in the wire is the electron charge density times the average speed of the electrons times ... | {
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Covariant formulation of electrodynamics IMO 'covariant formulation' of electrodynamics means that the equations should remain invariant across different Lorentz frames. Now there are broadly two ways to write electrodynamics equations.
*
*using 3 vector notation
$$
\frac{\partial \rho}{\partial t} + \nabla.\mathbf{... | It's true that the first equation has the same form in all Lorentz frames, but it's not obvious unless you know how $\rho$ and ${\bf J}$ individually transform. For example, the similar-looking equation
$$ \frac{\partial \rho}{\partial t} + k\, {\bf \nabla} \cdot {{\bf E}} = 0$$
(where $k$ is some constant) would not ... | {
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Why does the Earth accelerate upward, according to Einstein? I recently watched a video on the YouTube channel PBS Space Time which was called "Is Gravity an Illusion?". In this video, the host explains that Einstein claimed that it is not the apple that accelerates towards Earth but the other way around. In Newton's t... | Well, the thing is, if we want to analyse the motion an object, we need an inertial frame of reference. By equivalence principle, free-falling objects are inertial frame of reference.
So we have to analyse it from that point of view. But one of them should move, right? To get the visual. So, it's supposed that the eart... | {
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Lagrangian of the Euler equations Do the Euler equations (where $I_1,I_2,I_3$ are principal moments of inertia):
$$I_1\dot{\omega}_1+(I_3-I_2)\omega_2\omega_3=M_1$$
$$I_2\dot{\omega}_2+(I_1-I_3)\omega_3\omega_1=M_2$$
$$I_3\dot{\omega}_3+(I_2-I_1)\omega_1\omega_2=M_3$$
in their above general form have a Lagrangian? If n... | They do. In the case of the symmetric top with $I_1=I_2\ne I_3$ for instance, the kinetic energy is given by (if my algebra is right)
\begin{align}
T_{\hbox{rot}}&=\textstyle\frac{1}{2}\sum_k I_k\omega_k^2\, ,\\
&=\textstyle\frac{1}{2}I_1\left((\dot{\theta}\cos\psi+\dot{\psi}\sin\theta\sin\psi)^2+
(\dot{\phi}\cos\psi... | {
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Why do power lines use high voltage? I have just read that using high voltage results in low current, which limits the energy losses caused by the resistance of the wires.
What I don't understand is why it works this way. Does it have anythnig to do with electromagnetic induction in the wire which resists the current?... | If the total resistance of the transmission line leading from a power station to you is $R$ and the city/town you're in demands an average amount of power $P$. Then $P=I\times V$ . This makes the current drawn by the city/town is $I=\frac PV$ and so the higher the transmission line voltage, the smaller the current. Th... | {
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How is the curl of the electric field of a dipole zero? For a static charge, the curl of the electric field is zero. But in the case of a static dipole the electric lines of force curl. How it that possible?
| The electric field of a dipole has zero curl; this is easy to verify because it is (the $d\to0$ limit of) a superposition of two monopole Coulomb fields with zero curl. If you want something more explicit, then simply start with the explicit electric field,
$$
\mathbf E=\frac{1}{4\pi\varepsilon_0} \frac{3(\mathbf p\cdo... | {
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How do we apply Ampère's law for non-planar loops? How do we apply Ampère's (magnetism) law for non-planar loops?
Its most general form(or you can say the only one I know) is
$$
\oint_C \mathbf B\cdot\mathrm d\mathbf l = \mu_0 \iint_S\mathbf J\cdot \mathrm d\mathbf S
$$
But what would current enclosed mean in case of n... | This is relatively standard materials, so for the details you can consult your favourite EM textbook, but I'll sketch the overview.
The problem with Ampère's law, for any kind of loop (including planar loops!) is that there are plenty of surfaces $S$ that share the same boundary $C=\partial S$, which makes the statemen... | {
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Why is the Voltage across a Inductor not equal to 0 when the switch is closed?
I have such a diagram and at time t = 0 the switch closes, need to calculate the voltage across an inductor.I know that the Current across the inductor is 0 But the voltage across the inductor is not 0 but -120. But that does not follow ohm... | An inductor is not an ohmic device that is it does not follow $V= IR$.
It instead follows equation $V = L\frac{dI}{dt}$,
Since
Just when switch is closed $I$ is instantaneously $zero$ , it has started increasing this change in current leads to potential difference across inductor
Hope it helps
| {
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What makes the number of neutrons the number of proton similar? In basic chemistry, we are taught that an atom has roughly the same number of neutrons and number of protons, this doesn't seems to hold for larger atoms, but it is always roughly proportional (i.e. you seldom find an atom with 100 protons but 1 neutron, t... | You probably know that the electrons in atoms occupy a series of energy levels, the $1s$, $2s$, $2p$, etc orbitals. Although the structure of nuclei is complicated, basically the same idea applies to nuclei as well as atoms.
This happens because you can't put more than one fermion into the same quantum state. The elect... | {
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Why during annihilation of an electron and positron 2 gamma rays are produced instead of 1? $1 \gamma \rightarrow 1 e^- + 1 e^+$ (pair production)
Then why
$1 e^- + 1 e^+ \rightarrow 2 \gamma$ (annihilation of matter)
instead of
$1 e^- + 1 e^+ -> 1 \gamma$ ?
| The gamma photon should move with $c$, in any reference frame. Thus, it has to have a nonzero inertia.
But in the center of mass of the $e^-$ and the $e^+$, they have zero summed inertia.
Inertia is conserved, thus the resulting gamma photon should have zero inertia. It is impossible.
Ext:
If their spins are into the s... | {
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A rod is moving in space and an insect is on it. How many degrees of freedom does the insect have? Is the answer 7? The number of degrees of freedom of a system can be viewed as the minimum number of coordinates required to specify a configuration. Applying this definition, we have:
*
*For a single particle in a pl... | 5 for rod and 1 for point insect... total 6
| {
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Do particle and antiparticle annihilate when they meet? Do particle and antiparticle annihilate when they meet? As we know, an electron and a positron will annihilate when they meet. However, many quarks and antiquarks do not annihilate, but coexist as mesons. For example, a neutral pion $\pi^{0}$ is made up of $u, \ov... | The meson you describe are made up of a quark and its antiquarks and are called quarkonia. Of course, all mesons are unstable, but they do not necessarily decay via annihilation.
When you say "annihilate", you probably think of a process
$$ q\bar q \longrightarrow \text{single intermediate particle}\longrightarrow \te... | {
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Is the diffraction pattern of a vertical slit horizontal? I am familiar with the mathematical aspects of single slit diffraction pattern, at the undergraduate level.
Consider the following pictorial representation from the book Optics, by Hecht:
The fact that I find puzzling here is - even though the slit is shown ver... | The wider a slit, the narrower the diffraction pattern. So it makes sense that a tall rectangular slit makes a wide rectangular pattern.
| {
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Trolley problem
A trolley of mass $300kg$ carrying a sandbag of $25kg$ is moving uniformly with a speed of $27km/h$ on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of $0.05kg/s$. What is the speed of the trolley after the entire bag is empty?
I do not... | First Rule of Conservation of Momentum problems and Momentum Change problems: Define what the system is! Second Rule: Don't change the definition in the middle of solving the problem.
In this case, one could define the system as the trolley plus sand. So it's simple to calculate the total momentum of this system.
In... | {
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Equations of Motion for a Passive Suspension System I am trying to develop the equations of motion for a passive suspension system. The system consists of one mass connected to another mass via a spring and dampener system, and then the bottom mass is connected to the road via the tire which is modeled as a spring. I'm... | You are correct : the force is supplied by the bumps in the road.
The shape of the bumps and the speed of the vehicle produce a time-varying compression $x$ of the tire. The compression force is related to the compression $x$ and spring constant $k$ of the tire by $F=kx$. This force $F$ is transmitted to the masses in... | {
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What is spacetime (simple explanation)? Can someone please explain concept of spacetime in simple language? What is it and how it is important in the universe?
Wherever I have tried searching this concept, I have come across most complicated explanations.
A simple example will be appreciated.
| You can think of spacetime as a map. If you want to meet someone in this universe you have to agree an exact location and a time on the map. If you show up at correct location but at the wrong time then you are in the wrong place on the spacetime map.
| {
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A free-fall electron I am reading Wheeler and Taylor's Spacetime Physics. In Ch2, Wheeler mentioned:
"for gravity, any free-fall frame is an inertial frame." (roughly)
I am left wondering if that is true for electrical force:
Consider one charge is under a statistic electrical field. The charge is in free-fall. Is t... | An object is in an inertial frame if no forces are acting on this object. If you feel weightless than you are in an inertial frame. So jumping down from a wall you are for a moment in an inertial frame.
Such a definition of the inertial fram implicates two things:
*
*The gravitational pull isn't a force. Gravitation ... | {
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Opposite of particle decay I have read about particle decay, a process in which one particle becomes several other particles. However, I have not been able to find much information about its opposite: several particles combining into one particle. Is such a process possible, and if so, under what conditions? For exampl... | As Nick says, in laboratory conditions the crossections are very very small. In a way two body resonances are the only reversible example with high probability to study in the laboratory.
In the grand cosmological laboratory of the universe, in its history at the hadron epoch:
In physical cosmology, the hadron epoch... | {
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How do you calculate the resulting magnetic field for multiple sources? I've been looking at some fusion reactors and I keep wondering how putting some kind of extra magnet in some configuration would affect the field, but I don't know how to figure it out. Like for example if you took a solenoid and sat a permanent ma... | You are correct, they follow superposition. The magnetic field is a vector field, and so they follow a vector sum when they are in a superposition.
Maxwell's equations are linear ($\nabla \times$ and $\nabla \dot{}$ are linear operators) and it follows that solutions ($E$ and $B$) obey the superposition principle.
| {
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General relativity: How is the 4-velocity and momentum defined in GR? I know that in SR, the 4-velovity $$ u^\mu = (d t/d \tau,d x/d \tau,d y/d \tau,d z/d \tau ) $$ and $$p^\mu = m u^\mu.$$ How do these generalize to GR? I imagine there are new complications, particularly by what we let $p^0$ be. And are these only def... | Are you mentioning $p^0$ because you think of it as the energy?
If that is where your question is coming from, then perhaps this answer may be of use. Energy is something that an observer measures about an object. Let me explain.
The observer has a 4-velocity, $u^\mu_{\text{obs}}$, and the object has a 4-momentum, $p^... | {
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How did Rutherford conclude that most of the mass (as well as the positive charge) was concentrated in the nucleus? Geiger and Marsden's experiment led Rutherford to believe that the positive charge and most of the mass of the atom was concentrated in a small region. I understand what led him to conclude the way the po... | Wikipedia explains this rather well but I'll pick out the relevant stuff for you.
Before the Geiger–Marsden experiment, the general idea was that atoms were built of some permeable positive substrate in which some negative particles were floating around; the so called plum-pudding model.
If we shoot $\alpha$ particles... | {
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What causes the dark bands in water wave ripples? I was filling the bathtub the other day with water and noticed something. When calm, the light illuminates everything and I can see the sides and bottom of the white tub without shadows. Then, when I add a droplet of water its ripples (either its peaks or valleys of the... | What you see in a lensing effect by the ripples on the surface of the water. There will be regions on the surface where the water surface (like a crest) acts as a converging lens and regions where the water surface acts like a diverging lens (troughs).
Thus the illumination of your screen will vary.
You have made your... | {
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What is the relation between image velocity, object velocity and mirror velocity? Suppositions used:
Velocity of image = VI
Velocity of object = Vo
Velocity of mirror = VM
I Know the fact that VI=-Vo supposing mirror at rest
and VI=2VM supposing object at rest
Now considering both mirror and object in motion, VI=2V... | yeah the proper equation is 2Vm = Vi + Vo. now you need to choose an axis and put the proper sign for the two values. the equations will give you proper magnitudes and directions for the axis that you have chosen.
| {
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Have we directly observed the electric component to EM waves? For example, has anyone has directly observed charges oscillating due to standing EM waves? I am particularly interested because it'd demonstrate that radiation has a transverse electric component to it. Anything else (historical or modern) that shows that l... | Yes, we have observed, but not for all em waves. Detailed answer follows from “Planets and electromagnetic waves”.
Light waves or rays interact with electric fields of electrons in a solar cell to produce a disturbance in electrons so that electricity is produced. In a tungsten bulb, electrons try to move with very c... | {
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Why is the South Pole Telescope located exactly at the South Pole? I read that there is less atmospheric interference for the telescope at the South Pole because the atmosphere is thin and there is less water vapor in the air. However this seems to be true for many locations on Antarctica? Are there any other reasons t... | If the telescope was situated directly on the southern axis of the earth's rotation, the telescope's declination axis would be at zenith. The base for the axis would be level to the ground. In theory you could compensate for the earth's rotation with only one motion of the telescope. Also, its the only place on earth ... | {
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Why do we equate an indefinite integral to a specific value? Suppose we want to obtain a displacement vector defined as $\mathbf s(t) = x(t)\mathbf i + y(t)\mathbf j + z(t)\mathbf k$ from the components of a velocity vector $\mathbf v(t) = \dot x(t)\mathbf i + \dot y(t)\mathbf j + \dot z(t)\mathbf k=\mathbf 0$. Accordi... | You are being confused by the shortcut that people took who wrote that expression. They mean for the integral to be taken between definite limits.
It would be more proper to say
$$x(t) = x(0) + \int_0^t \dot{x} dt$$
But that gets longwinded. Most people, when seeing the expression as you gave it, will understand it to ... | {
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Can we add attraction forces? From Newton's Law of gravitation we know that:
$$F=G\frac{m_1m_2}{d^2}$$
For simplicity, let's say that both $m$ are $1\;\mathrm{kg}$ and that the distance apart was $1\;\mathrm{m}$. Yielding $G$ as the attraction force in Newtons. Hence $F= 6.67\times 10^{-11}\;\mathrm{N}$.
Now what if y... | If we consider the two masses of $1(kg)$ as point particles, then the force between them when they are $1(m)$ separated is $G(N)$.
The force between two point particles of $0,5(kg)$, who are also separated $1(m)$, is $0,25G(N)$. Now if we glue a point particle with mass $0,5(kg)$ to each of these two particles, the ma... | {
"language": "en",
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Principle of launching satellites into orbit I was reading in a book about the basic concept of launching satellites into orbit. I came across a paragraph saying,
If we take a body high above the surface of the earth, and then project it with some horizontal velocity, it will describe a parabolic path and fall back on... | The paragraph is correct but a bit ambiguous. Imagine a wall of height 'h' amidst a fountain or lake of certain radius. If now you increase the horizontal velocity such that it crosses the fountain, then your job is done. Replace the fountain or lake with earth and cliff with that particular height where they project ... | {
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What is the difference between $\psi$ and $|\psi\rangle$? My understanding is that $\psi(\vec{r}, t)$ and $|\psi(\vec r,t)\rangle$ are the same thing yet one expressed as a wave function and the other expressed as a vector in the Hilbert space. Is this true? Or is there a deeper difference between the two notations?
| $\psi (\vec{r},t) $ is like you said, just a way to express the vector $|\psi (t)\rangle $ in 'position space', mathematically expressed like is written in the comments:
$$ \psi (\vec{r},t) = \langle \vec{r} | \psi(t) \rangle = \int \delta(r'-r)\psi(t) d^3 r $$
| {
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Fluid Dynamics in a Syringe I am currently working on a project where we use syringes to extrude some viscous materials. I will explain what I am trying to do and I just want to know what size of tubing would be better for me. I have a 10 cc syringe connected to 3/32" tubing with luer lock and at the very end, it is at... | please check the syringe plunger tip (the black rubber thing on the end of the plunger shaft). In contact with certain fluids, the plunger tip tends to adhere to the syringe cylinder walls and break loose suddenly, then get stuck again, break loose, etc. as you push on it. the fluid then spurts out suddenly, stops, spu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328193",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What determines invariant mass? The only answer I have been able to find is that energy determines mass but photons have energy yet are still massless. Furthermore this then leads to the question of what determines invariant energy, which I would think to be mass. So in total what are the circumstances that determine f... | Answer: If a particle has energy $E$ and momentum $\vec{p}$, its invariant mass is given by $m=\frac{1}{c^2} \sqrt{E^2-p^2c^2}$, where $c$ is the speed of light.
Explanation:
Momentum and energy of a particle change as the particle moves faster or slower. Equivalently, the energy and momentum that you the observer m... | {
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Can I tell if I'm being attracted by a gravitational field by checking if my time is dilated relative to an observer? Due to the equivalence principle of GR, we know that gravity and acceleration are indistinguishable from each other. We also know that a gravitational field causes time dilation, but accelaration does n... |
We also know that a gravitational field causes time dilation, but accelaration does not.
In the 'elevator pulled upward in outer space with constant acceleration' thought experiment, a photon emitted from some process at the bottom of the elevator is received at the top with a longer wavelength than a photon emitted ... | {
"language": "en",
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Could a planet with a strong magnetic field exert a diamagnetic force on an orbiting moon? Here is a question from the world building stack exchange.
https://worldbuilding.stackexchange.com/questions/79003/making-a-slow-orbit-around-a-large-gas-giant
Requested: a means to have a moon of Jupiter orbit closely but slowly... | A nice, realistic example of this is for Ganymede at Jupiter. The Jovian magnetic field is ~0.42 mT at the planet's equator and the orbital speed of Ganymede is roughly 10 km/s. If we take a hand-wavy approach with the Lorentz force assuming a 1 coulomb charge, we get a maximum force of ~4 newtons.
For Ganymede this ... | {
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Why are stars spherical whereas (some) galaxies are disks? I read here that galaxies become disks if there is a lot of gas in them, since their angular momentum is conserved while their energy decreases due to collisions of the gas particle. I have two questions about this:
*
*Why is the disk the configuration that ... | The stars were roughly disk shaped as the nebula that formed them was collapsing. The matter in galaxies is much more sparse. The thing that keeps them disk shaped is the centrifugal force as the stars and other bits orbit around each other and around the galaxy, and continually miss each other, otherwise, the galaxy w... | {
"language": "en",
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"source": "stackexchange",
"question_score": "8",
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Which Liquids freeze when combined? Are there any liquids (or liquid and solution) that when combined react to where they will freeze?
| Good question, but you would probably receive better attention, information on the chemistry stack exchange.
I don't know the answer regarding two liquids, but if you mix the two solids, Barium Hydroxide Octahydrate and Ammonium Thiocyanate, the solids will spontaneously fuse into a liquid with an endothermic reaction... | {
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What is "velocity distance" in astrophysics? I was reading some papers on astrophysics, and in several of them, I've encountered velocity being used as distance. Or more precisely, distance being in dimensions of distance over time. For example, a paper referred to a group of galaxies at "roughly $2000\:\mathrm{km\:s^{... | Hubble's law will convert the velocity to a proper (as opposed to co-moving) distance for you; indeed Wikipedia states one form of Hubble's law as:
"... the observation ... that ... Objects observed in deep space (extragalactic space, 10 megaparsecs (Mpc) or more) are found to have a Doppler shift interpretable as re... | {
"language": "en",
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Degrees Of Freedom of Spring-mass system
Consider 2 masses $M_1$ and $M_2$ connected with a spring of stiffness $k$, resting on a smooth frictionless surface. Now, each mass has its own 1 DOF along the $x$-axis. And the system has 1 constraint , i.e. the spring.
So, in all there should be 2(1)-1= 1 DOF for the system... | Both m1 and m2 (ie, the system) is a two-dimensional case. Then, m1 and m2 each possess 2 DOF. Hence total DOF of system = 4
No: of constraints on m1= 1
No: of constraints on m2= 1
So, total constraints of the system= 2
Hence, resultant DOF of system= 4-2
=2
| {
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Non-analyticity of the modulus function I'm studying the Ginzburg-Landau theory of superconductors, and I have read that the free energy can not depend on odd powers of the modulus of the order parameter $\psi$ because $| \psi| = \sqrt{\psi_x^2 +\psi_y^2}$ is not analytic at $\psi = \psi_x +i \psi_y = 0$. How do you sh... | Hint: the function
$$
f:x\mapsto\sqrt x
$$
is not (real) analytic at $x=0$ (why?).
| {
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Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$?
Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity so the line of action coming out of the plan... | @JerrySchirmer's advice is generally good, and worth heeding. If you actually construct the free-body diagrams for a particle on an inclined plane and your particle on a cone, you will note the following important difference:
*
*A particle at rest on an incline (or sliding down an incline) has an acceleration vecto... | {
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Does an increase in entropy always result in an increase in heat, or can there be increased entropy without an increase in heat? Most situations I can think of where entropy increases also results in an increase in heat, but just wondering if that is a rule. Are there any cases where heat does not increase with entropy... | In addition to the answer provided by @Deep, there are situations where a system can have negative temperature. In such situations, the system can release heat and increase entropy. This can happen when there is a maximum energy that some degree of freedom of the parts of the system can assume. The canonical example fr... | {
"language": "en",
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Tension direction for pulleys in connected mass systems I got caught up with a conceptual question dealing with a practice problem with connected mass mechanics.
Looking at the solution lecture notes is the following image for the Free Body diagrams for each mass, and the pulley, respectively:
Obviously, the Free Bo... | Strings cannot push unlike a coiled spring.Hence if we show the forces acting on a point due to a string the tension has to be pulling that point not pushing it.
| {
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Can a current be induced in this coil-magnet configuration? Coil is moving around ring magnet made of two arch shaped magnets with poles opposing each other like so:
Would a current flow in coil? or be canceled out?
| Yes, it will be ac voltage and current. You see that as magnet plate rotates, the coil will be moving in to the lines of flux in the air gap. As it starts to cut true the lines, the voltage will increase to a maximum and decrease as is leaves the gap. it will do this twice per turn. Say the magnets turn at 30 times... | {
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What is the energy of a single charge system? I will try to limit the question in the case of the electric fields, but is something that applies also to the magnetic ones.
There are two ways to express the energy in a capacitor:
*
*By Voltage : $U = 1/2 CV^2 $
*And by Field : $U = 1/2 \varepsilon E^2Ad$, With Ener... | The capacitor stores its energy in form of electric field.
Initially both the plates were neutral. After applying the potential difference, electrons move form one plate to another.
So to calculate the energy, you would first take a charge $dq$ from one plate to another. By this action, you just created an opposite c... | {
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Size of mercury barometer and effect on its reading I was thinking that since atmospheric pressure is 760mmHg what would happen if I shrink a mercury barometer until it's shorter that 760mm in height. What would happen? Would the barometer retain it's ratio of mercury height? Will the mercury fully fill the barometer? ... | A mercury barometer is designed to measure the difference in pressure between the surface of the mercury outside the tube and the surface of the mercury inside the tube.
The space inside the tube is filled with mercury vapour and hopefully nothing else.
The column of mercury is kept in position because the pressure exe... | {
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Why young modulus value doesn't change even if we change the parameters? The Young modulus of steel is determined using a length of steel wire and is found to have the value EE. Another experiment is carried out using a wire of the same steel, but of half the length and half the diameter.
What value is obtained for the... | Young's modulus is a material property and independent of the size or shape of the specimen being tested
| {
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Would seawater lose their ions after sliding across graphene Accroding to this http://www.iflscience.com/technology/how-drop-seawater-graphene-generates-electricity/ webpage, voltage would be generated if droplets of seawater (which contain ions) are dragged across the surface. However, there is no mentioning of what ... | According to the model explained in the paper (Generating electricity by moving a droplet of ionic liquid along graphene), the water droplets retain the Na+ and Cl- ions.
The mechanism is as follows:
When a NaCl droplet is put on a strip of graphene, a double layer of Na+ ions (purple) forms at the interface. These pos... | {
"language": "en",
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Field due to internal Induced charge on a conductor to an external point? A charge q is located at a distance r from the center of a conducting sphere with inner radius 2r. The charge induces charges on the inner surface of the sphere according to Gauss' law .
The electric field at point p is to be approximated.
Inside... | There are three types of charges contributing to the field at point P
*
*The charge q itself
*The induced charge on the inside of the sphere
*The induced charge on the outside of the sphere.
First, the contribution due to the charge q itself will have a magnitude of $\frac{kq}{r^2}=\frac{kq}{(4R)^2+(1R)^2}=\frac... | {
"language": "en",
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Are there experiments that deal with the headlight effect? If I am not mistaken, the Ives-Stilwell experiment measures the frequency of emitted light to test the relativistic doppler formula.
Is there anything like this for light intensity? Have we measured the headlight effect?
Anything like precision tests that are... | The angular distribution of products from decay-in-flight beams such as those used to generate neutrino beams and radioactive beam accelerators (PDF link) are a sensistive test of this prediction.
I don't know of a paper discussing the focusing specifically (because I am an end user rather than creator of such beams an... | {
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Questioning validity of SHM of vertical mass-spring system Horizontal mass spring system is good but vertical mass spring system confuses me.
Q1. Can there be two restoring forces in an SHM?
Q2. If no, then weight of mass seems to disturb SHM as down extreme position below the mean position would be much farther than... | On applying a constant force in an SHM,it only changes its mean position BUT its amplitude,time-period, max velocity etc remains same.This can proved by solving the differential equation given below:
$$\frac{d^2x}{dt^2} = \frac{-kx}{m}+g$$
(solution of above differential equation left to you)
On solvi... | {
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Is the huge calcite birefringence accounted for by first principles? The birefringence in calcite is huge (possibly the largest?). The question is, why is it so special? why is such kind of materials so rare?
In other words, is it explained by first principles?
By google, I just found a paper predicting the birefring... | The size of the birefringence of calcite is not surprising. It has a crystal structure in which all the planar carbonate ions have the same orientation. The polarization of planar ions is much larger for electrical fields in the plane (light coming in perpendicular to the plane) than for electrical fields perpendicular... | {
"language": "en",
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Would a handspinner spin indefinitly in space? I'm having a argument with a colleague, I don't know how to explain to him that if you spin a handspinner in space it will spin indefinitly (if you don't hold it). I agree that if you hold it, it will slow down because of the friction with the center part.
Would it theoret... | Assuming that the engineering is perfect, that is, your handspinner can't be broken, that would be the case in the vacuum. It stops on Earth because of the friction with the air.
| {
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Well-defined momentum I have a question which states:
Show that a particle can have a well-defined momentum in every energy eigenstate if and only if the potential energy is uniform in space.
I am completely unsure how to start. The Schroedinger equation states:
$\frac{p^2}{2m} \psi+V(r)\psi=E\psi$
$p^{2}=2m(E-V(r)... | A partial answer starts with the observation that, if the particle has a well-defined momentum, then
\begin{align}
\hat p\psi(x)&=p\psi(x)\, ,\\
\hat p^2\psi(x)&=p^2\psi(x)
\end{align}
If $\psi(x)$ is an energy eigenstate, then $\hat H\psi(x)=E\psi(x)$. Thus
\begin{align}
\left(\hat E-\frac{\hat p^2}{2m}\right)\psi(x)... | {
"language": "en",
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Proof that Verlet integration conserves energy I was reading about different integrators that one might use to solve the system of differential equations which governs the $n$-body problem. I read that the Verlet integrator is time-reversible, and thus conserves energy.
I don't understand why time-reversibility implie... | Firstly, the Verlet integrator only conserves energy in the limit $\Delta t\to 0$. In practice it produces energy drift, although the long-term energy drift is smaller than for most integrators.
Regarding your question, the gist of the argument is that integrators that are not time-reversible do not exhibit so-called a... | {
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How to explain the relationship between wave's amplitude and intensity? I have the following statement which I don't know how to explain:
Suppose I have 2 identical monochromatic waves (same intensity and phase) shooting into the same receiver. If each wave's intensity is I, based on energy conservation I would expect ... | As explained here, you have to consider the fact, that your light waves' amplitude gets averaged over a certain amount of time, thus decreasing the intensity.
I quote from the website, just for the sake of having the information close to this question:
"Try this: Let $ψ=Acosθ_1$ and $ϕ=Bcosθ_2$.
Then: $I∝(ψ+ϕ)^2=(Acos... | {
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Why the name 'displacement' operator? I'm studying coherent states of the harmonic oscillator and I have learned about the so called displacement operator, which is the operator defined as
$$D(\alpha) = e^{\alpha a^\dagger -\alpha^* a}$$
whose action over the fundamental state $|0\rangle$ is to produce a coherent state... | A coherent state is characterized by a complex number $\alpha \in \mathbb C$.
Applying the displacement operator $D(\beta)$ to $|\alpha\rangle$ translates $\alpha$ in the complex plane by $\beta$, in the following sense:
$$ D(\beta) |\alpha\rangle \sim |\alpha+\beta\rangle . \tag 1 $$
Here, $\sim$ means "up to a phase"... | {
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Where does the force actual act?
Why are the two mass of $m_1$ and $m_2$ not multiplied by minus one?
I know that two minus multiplied gives you plus by but I mean the two masses are attracting so they should have a sign like so $$F_g=\frac{G(-m_1) \times (-m_2)}{r^2}$$
I ask these because equation would actual give t... | In reality the force acts on all parts of $m_1$ and $m_2$ but it varies due to the variation in distance for different areas of $m_1$ and $m_2$. In practice though, if $m_1$ and $m_2$ are spherical, the force can be assumed to act at the center-of-mass of each.
| {
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Can anyone tell me that actually What vector multiplication is? I am a high school student. Yesterday I attended a lecture on vector multiplication (first time). There was something I was not able to understand.
The only concept of multiplication I had before is 2x3=6, means that if we write '3' 2 times we'll get 6.
Bu... | A Geometric View of Vector Products
Vectors have geometric properties independent of coordinate systems. The vector dot product $\mathbf A \cdot \mathbf B = AB \cos(\theta)$, projects the length of vector $\mathbf A$ onto the direction of vector $\mathbf B$; it is the shadow projection of the one vector onto the othe... | {
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Why are Grassmann fields never classical? I see this statement in many QFT books (e.g. Altland & Simons' Condensed Matter Field Theory) but the author never explains why.
Can you briefly explain why Grassmann fields never have a classical meaning (preferably physical arguments) and possibly point out some good referenc... | I have proposed a classical interpretation for a pair of Dirac fermions in arxiv:0908.0591. It is a lattice version, works only for a pair, not a single fermion, requires a preferred frame, and the Hamilton operator for the classical $\mathbb{Z}_2$-valued field is only an approximation of the lattice Dirac operator.
... | {
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How do we realise the wave for an electron orbiting a nucleus in its first orbit as per bohr model? How do we realise the wave for an electron orbiting a nucleus in its first orbit as per bohr model?
As per my textbook, we can account for as to why angular momentum is quantised. But I fail to understand what would the ... | Maybe the term "orbiting" causes some problems. The electron is not moving around the nucleus as bohr assumed (he had no solution according to the problem that an electron on a circular orbit should emit electromagnetic waves and crash into the nucleus).
You should think about the elcetron as part of the whole system ... | {
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"answer_id": 1
} |
How to prove the constant speed of light using Lorentz transform? I read the light-clock example in my book which proved the time dilation formula by assuming that the speed of light is constant for all observers. But I've trouble in understanding it the other way around. Lorentz transformation is just a correction to ... | An enlightening (but possibly advanced) method to prove the constancy of the speed of light from the Lorentz boost transformation is to find the eigenvectors of the Lorentz boost. Two of the eigenvectors are along the light cone. The corresponding eigenvalues are equal to the doppler factor and its reciprocal.
(These e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/334884",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 6,
"answer_id": 2
} |
Covariant derivative 1+3 formalism I can't find the proof for the following equation:
$$ \nabla_bu_a=D_bu_a-A_au_b $$
where $D_b$ is the spatial derivatives respect to $h_{ab}=g_{ab}+u_au_b$ in the 1+3 formalism and $A_a=u^b\nabla_bu_a$.
EDIT:
I want to see it by computation: I start from $h_{ab}=g_{ab}+u_au_b$ and ... | Assuming $u^d$ is the unit normal vector to the hypersurface, we have $u^du_d=-1$, implying
$$0=\nabla_a(u^du_d)=u_d\nabla_au^d+u^d\nabla_a u_d.$$
Then, using $u_d=g_{db}u^b$ and passing $g_{db}$ through $\nabla_a$, we see
$$2u^d\nabla_a u_d=0.$$
The last two terms are of this form, hence vanish. The first is the one... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/335114",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Heisenberg Uncertainty Principle Applied to an infinite square well I appreciate the statement of Heisenberg's Uncertainty Principle. However, I am a bit confused as to how exactly it applies to the quantum mechanical situation of an infinite square well.
I understand how to apply Schrödinger's equation and appreciate ... | This question is actually almost identical to a question I had in my first year quantum mechanics course. It posed that a hypothetical friend asked you why having definite energy in the infinite potential well doesn't violate the uncertainty principle. Here I will provide you with the answer I gave all those years ago.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/335184",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 5,
"answer_id": 3
} |
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