Wave Definition and 999 Threads

Does mean velocity of particle equal group velocity of wave packet in QM?If they do not equal which of them is classical velocity?

It is a rather simple question: In my textbook it writes something like: $$\frac {\partial \Psi} {\partial t}= \frac{i\hbar}{2m}\frac {\partial^2 \Psi} {\partial x^2}- \frac{i}{\hbar}V\Psi$$ $$\frac {\partial \Psi^*} {\partial t}= -\frac{i\hbar}{2m}\frac {\partial^2 \Psi^*} {\partial...

since, in order to view the shape changes in our wave packet we are presented with the taylor expansion of the frequency ω(k) = ω(k0) + (k − k0)dω/dk + 1/2*(k − k0)^2 (d^2ω/dk^2) we are told that only the third term that is the 1/2*(k − k0)^2 (d^2ω/dk^2) contributes to change in shape of the...

They say wave function is different to quantum field. Then what is the difference between EM wave and EM field?(By the way :Is that EM wave the wave function of photons?).It seem to me EM wave is the wave of EM field?

why the general wave vector q (in the proof of Bloch theorem in Ashcroft Mermin) is represented by k-K, where k is in the 1st BZ ? why not q=k+K ( usual vector form) what is special about k-K?

I´´m confused. How can a single photon in the lightspectrum with wavelength of a few hundert nanometers go through both slits in the double slit experiment at the same time. I understand the wave- particle duality and the concepts in principle. My confusion is in the context of little wavelength...

We know that the non-relativistic propagator describes the probability for a particle to go from one spatial point at certain time to a different one at a later time. I came across an expression (lecture notes) relating ##\Psi(x,t)##, an initial wave function and the propagator. Applying the...

Reading the classical Feynman lectures, I encounter the formula(19.53) that gives the radial component of the wave function: $$ F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k $$ that, for ##n=l+1## becomes $$ F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n $$ To find ##a_n## I...

The question arose when watching Sean Carroll video: The Biggest Ideas in the Universe _ Q&A 6 - Spacetime 3:50 - 13:30 Because photons follow null geodesic in spacetime the question arose from viewers: "photons do they really experience no time this is a question" And in the answer: "but if...

When the delta t and x approached zero, assumably it results in the whole fraction to be zero. The slide shows it will be ##k^2##. Can someone explain this to me, please? P.S. I have tried to search this up, I could not find anything related to the confusion.

A common equation for an electromagnetic wave is Ey = Eocos(kx - wt + phi). According to this equation, wouldn’t the intensity of the electric field extend indefinitely in the y-direction? How does this make sense?

does an em wave with circular polarization behave like a coil, i.e. do perpendicular electromagnetic fields join internally? I am very confused on this subject

c^2 * t^2 = x^2 + y^2 + z^2 = r^2

I understand that because the vectors are perp, k x i = j, but why is k x j = -i? Why the minus? Could you please explain?

That is the diagram of the question. How is the reflected going to be?

Summary:: Given an equation of geopotential of wave in a westerly flow, take derivatives to derive general expressions. Given an equation of geopotential of wave in a westerly flow, take derivatives to derive general expressions.

When studying classical mechanics we are told that light is the propogation of electromagnetic waves. This makes perfect sense, as I can imagine these fields behaving this way, and in turn have an associated wave length. When learning about QM, I have heard that the wavelength of a (any)...

Hello there. I set up the problem like this, I have a wave incident from air on the anti-reflective coating consisting of: ##\tilde {\vec E_I} (z,t) = \tilde E_{0_I} e^{i(k_1z- \omega t)} \hat x## ##\tilde {\vec B_I} (z,t) = \frac 1 v \tilde E_{0_I} e^{i(k_1z- \omega t)} \hat y## This wave gets...

I've been having an issue with understanding the convention of wave direction notation, here is my current understanding where I am at currently: A 3D harmonic solution to the differential wave equation can be given as: If we make some assumptions about the wave, that its amplitude is 1, its...

I saw this statement from the textbook "Quantum physics of atoms, molecules, solids, nuclei, and particles" second edition pg 166. According to the text, is the author saying the solution to the TISE is the eigenfunction and when you multiply the time dependent part, you get the wave function? I...

I currently do amateur stellar spectroscopy, low to medium resolution, and I like to expand further to study magnetic fields near the sun. I just started studying plasma physics and am aware of Alfvén waves. How would these be observed on a spectrum.? Would it be oscillating Ha lines, or...

In classical mechanics, we have either Newton’s laws or a Lagrangian in terms of coordinates and their derivatives (or momenta) and we can solve them for the behavior of the system in terms of these variables, which are what we observe (measure). In QM, we quantize classical mechanics by making...

Yeah, as I said, i have no idea why we can assume beta to be the same for any position at given alpha.

This is dumb question, so please bear with me. In the double-slit experiment where they fire a single electron at time, as you can see the electron gun fires a single electron. Now the electron travels as a wave. Now my question is, why doesn't the wave collapse when the wave encounters...

I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?

Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?

Taken into account the transverse nature of the wave, I deduce the particle must move of harmonic motion from maximum amplitude ##A## to negative maximum amplitude ##-A##. The period ##T=\frac{1}{f}## is equal to the time in which a particle travels a distance ##d=3\cdot A##. I then approximated...

For any physical theory to be accepted, the consensus is that there must be a radical categorical separation between the formalism in which the theory is described (using exact mathematical language) and the empirical situation in which it is validated (using real world tools, materials and...

I got that the sound wave will take 0.3s between the student and the left wall. It takes 0.5s between the student and the right wall. The first time these waves will coincide is 1.5s (5 trips for left side and 3 for right side). I then did 1/1.5 to get 0.67Hz. However, the answer is 6.67Hz. I'm...

What is an interpretation of wave of field(wave that its medium is field) in QFT?Is it correct that the trajectory that wave propagates is the "classical trajectory" of particle created by the field?

I read about the non-communication theorem and I understand why when changing one practical will not change the other . But suppose that there is two observers that doing the double slit experiment, but using it with two entanglement practicals. observer one should send signal of yes or...

For part a, I have the following $$\ket{p_0} = \varphi_{p_0}(x)=\frac{1}{\sqrt{2\pi\hbar}}e^{ip_0x/\hbar}$$ but I am totally lost on how to proceed.

I've been studying quantum mechanics this semester in school and have ran into an issue I can't find an answer for. I understand why we take the complex conjugate of the wave function, such as when calculating expectation values. I'm a little confused though as to why we take the complex...

I am quite confused by this. I was sure that ω=3*sqrt(5)*10^6, because that is the coefficient of t, and generally u(x,y,z,t)=Asin(kx−ωt+ϕ) for a multi dimensional harmonic wave. However in the answers it is said that ω=3*sqrt(5)*10^14. I can't see the reason for that, could anyone explain please?

I am trying to solve the following exercise. In a H atom the electron is in the state described by the wave function in spherical coordinates: \psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)} With a and \mu positive real parameters. Tell what are the possible values...

I answered the first part of the question where I estimate the radius of ##O_{2}## is ##\approx 1.5 \times 10^{-10} \ \text{m}##: $$ p = \frac{KT}{l 4 \pi r^{2}} = \frac{(20+273.15)(1.38\times 10^{-23})}{(0.1)(4\pi)(1.5 \times 10^{-10})^{2}} = 0.143 \ \text{Pa}.$$ The confusion arises on the...

[Mentors' note: This thread has been moved from the relativity forum, as it is a question about the classical behavior of waves] Is the length of a beam of light the number of crests times the wavelength?

In QM by virtue of wave function we calculate any things. But in QFT it seems that there is a lacking of notion of wave function.I do not understand why QFT still goes well(it is a good theory to calculate any things)?

For a physics project, I'm planning to investigate the relationship between the number of slits in a diffraction grating and the intensity of the central maxima. The light meter which I'm planning to use to measure the intensity gives me a result in LUX. I know the wavelength of the red laser...

If you want to detect a particle in the 2 slit experiment on a detector. And we state that the electron is traveling as a wave so there is a wave front...that must mean that the wave front hits the detector at the same time in more than one place where there is constructive interference. But...

Why is the divergence of an amplitude of an electric field of a monochromatic plane wave zero?

I am trying to solve a PDE (which I believe can be approximated as an ODE). I have tried to solve it using 4th Order Runge-Kutta in MATLAB, but have struggled with convergence, even at an extremely high number of steps (N=100,000,000). The PDE is: \frac{\partial^2 E(z)}{\partial z^2} +...

I draw this picture in order to solve this problem. My first attempt was find the hypotenuse of the triangle and divide it by the speed of sound wave. d=a/sin(θ) d=4483.43m t=d/c=13.07 sec However, I am not sure whether I did it correctly or not... It looks the time is too big as an answer... I...

https://phys.org/news/2020-09-function-collapse-gravity.html An interesting article I saw yesterday. However, both Nature articles (the summary [https://www.nature.com/articles/s41567-020-1026-2] and the actual technical paper [https://www.nature.com/articles/s41567-020-1008-4]) are behind a...

COMSOL gives me the impression that it always gives unrealistic solutions in time domain for wave problems, say mechanical waves or simply solutions of a wave equation. In frequency domain, COMSOL works better for wave problems. Anybody agrees?

Actually, maybe i am confusing something, or valuing unnecessary things, but this doubt arises and i am not sure how answer it. The reflection of an incident wave changes (suppose it will change, we don't need to talk when or why to go on the discussion) by π rad, but, this reflection lags the...

Would it be correct to say, that gravitational waves of the magnitude that is currently detected by LIGO and similar detectors, are prevalent to the extent that there is no single location in the known universe, that such magnitude of gravitational waves, don't pass through at least several...

A single electron sitting in a void has an electric field that spreads out evenly in all directions as far as there is open empty space to allow it, is this roughly a correct statement? Let's say we now introduce a singe proton into the void, 100 miles from the electron - it will also have an...