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Plane waves, angular momentum, and the 2D Schrödinger equation

I've been thinking about the 2D Schrödinger equation for a free particle, particularly in polar coordinates, and the particular solution $$\Psi(r, \phi) = J_1(r)e^{i\phi}.$$ This solution has an ...
bob.sacamento's user avatar
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33 views

Dispersion Relations in a Cold, Unmagnetized, Collision-less Plasma

Currently I am trying to understand the physics of waves in cold plasmas. So in a cold, collison-less, unmagnetized plasma you can derive two different different dispersion relations: one for ...
ReggiePlasmaQs's user avatar
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42 views

Plane Wave in a Periodic Lattice

From Introduction to Superconductivity; Second Edition; A.C. Rose-Innes and E. H. Rhoderick; Page 3 Electrons have, of course, a wave-like nature, and an electron travelling through a metal can be ...
Jbag1212's user avatar
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Calculating in-duct sound intensities from sound pressure measurements with mean mass flow

In the time domain and in free field condition the sound intensity can be calculated as $ \vec I(t)=p(t) \cdot \vec v(t)$ with $p(t)$ being the sound pressure and $\vec v(t)$ being the sound velocity. ...
Matthias La's user avatar
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1 answer
52 views

How to formulate the expression of this EM wave? [closed]

Consider a plane EM wave polarised parallel to the $(Oz)$ axis, this wave propagate in empty space with direction $\overrightarrow{OD}$ in the $(Oxy)$ plane with an angle $ \theta $ from the $(Oz)$ ...
HellBoy's user avatar
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70 views

What is meant by "bases" not belonging to state space and how are they possible?

Section A3 of Chapter II on mathematical basis of QM in Cohen-Tannoudji’s "Quantum Mechanics" book has me a bit confused. The section is named ...
Clerni's user avatar
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Fourier transform of $1/r$ with plane-wave expansion formula

I know that up to constant factors ($\pi$'s and such), the Fourier transform of the Coulomb potential $$\frac{1}{4\pi}\frac{1}{r}$$ in 3-dimensions is proportional to $$\int d^3\vec r\frac{e^{i\vec k \...
3KidsInATrench's user avatar
1 vote
0 answers
40 views

Plane wave expansion and time independence of Hamiltonian

I am confused by a statement made in "Lectures on Quantum Field Theory", 2nd edition by Ashok Das. The author is describing the interaction picture (IP) of QFT. In equation (6.52) he shows ...
baba26's user avatar
  • 513
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1 answer
60 views

Free and non-free Dirac's particles

In trying to understand evolution of Dirac particle in relativistic QM (not QFT) I have following guess that I don't know I'm correct or wrong? edited after solution of akhmeteli: It is well known ...
moshtaba's user avatar
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1 vote
2 answers
101 views

Intuition for $e^{i(px-Et)}$ rotating clockwise?

I can demonstrate it by example but it is very counterintuitive to me that the phase in $e^{i(px-Et)}$ rotates clockwise vs $e^{i(px+Et)}$ rotates counterclockwise as time increases. Is there an ...
nemui's user avatar
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Deriving relation between amplitude of $\vec{B}$ and $\vec{E}$ in EM waves

From the complex form of wave function of $\vec{B}$ and $\vec{E}$ (propagation along $z$) ie. $\vec{E}(z,t) = \vec{E}_0 \, e^{i(kz- \omega t)}$ and using the relation ${\vec\nabla \times} \,\vec{E} = -...
Prat Y's user avatar
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Coefficients for a multidimensional plane wave expansion [duplicate]

If I have, for example, $\psi_{n_x,n_y,n_z}=e^{\frac{\pi i}{L}(n_xx+n_yy+n_zz)}$ and $E_{n_x,n_y,n_z}=mc^2\sqrt{1+\frac{\frac{\pi^2}{L^2}(n_x^2+n_y^2+n_z^2)}{m^2c^2}}$ and I want to find the wave ...
Ryan Parikh's user avatar
2 votes
2 answers
476 views

Fundamental solutions and initial conditions (for d'Alembert operator)

I would like to understand the plane wave solution for the (3+1-dimensional) d'Alembert operator $$ \square = \nabla^2 - \frac 1{c^2}\frac{\partial^2}{\partial t^2}\tag{1} $$ in terms of its ...
Leonardo Rossi's user avatar
5 votes
2 answers
241 views

Omitting the negative exponential in the plane-wave solution of the Schrodinger equation

The time-independent Schrödinger equation in one dimension for a free particle, $$\frac{-\hbar^{2}}{2 m} \frac{\partial^{2} \Psi(x)}{\partial x^{2}}=\varepsilon\Psi(x)$$ can be solved as a homogeneous ...
Invenietis's user avatar
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Use the plane wave expansion to explain the fundamental limit of resolution?

As stated in the title I don't really understand how I can explain the fundamental limit of resolution using plane wave expansion. The question was asked by my professor and seems a bit vague to me. ...
Hikikomori's user avatar
7 votes
1 answer
1k views

Incoming and Outgoing Waves in Quantum Field Theory

I apologize if this seems like a simple question, but I have been agonizing over it recently. In nonrelativistic quantum mechanics, a plane wave of the form $e^{\pm i\vec p\cdot \vec x}$ is called ...
Daniel Waters's user avatar
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2 answers
67 views

How to derive the Electric field from the magnetic field?

Given a linearly polarized, monochromatic plane wave with $H = H_0y^{cos(kz − ωt)}$ traveling in the $+\hat{z}$ direction that is incident on a dielectric sphere with permittivity $e$ and radius $a$, ...
A P's user avatar
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For unpolarized plane wave traveling normal incident from air to dielectric what are the reflection and transmission coefficients?

Given an unpolarized plane wave traveling in air and hitting a dielectric at normal incident what equations can be used to calculate the reflection and transmission coefficient? I know for a polarized ...
A P's user avatar
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6 votes
3 answers
356 views

Why don't plane waves always expand according to Huygens' principle?

I have seen a few videos about Huygens' principle and I don't understand why a plane wavefront doesn't expand both vertically and horisontally. According to my understanding of Huygens' principle, ...
Hajen1000's user avatar
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1 answer
157 views

Magnitude of an Electric field as superposition of plane waves

I need to show the magnitude $u(x,y,z)$ of an arbitrary electric field can be written as a superposition of infinite number of plane waves travelling along different directions. Can someone provide ...
A Q's user avatar
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1 vote
1 answer
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Single gravitational plane wave or their interference can carry spin angular momentum?

I would be grateful if anybody could tell me if I had one gravitational wave in the form of a plane wave, it still would carry spin angular momentum? We know that gravitational waves are mostly the ...
Ali's user avatar
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3 answers
211 views

Why do most of the book represent Plane waves by considering a single sine or cosine wave? There should be many, right? Isn't it misrepresentation?

This Image is from Electrodynamics by Griffiths. Here also a monochromatic electromagnetic wave is considered.
Tarun Garg's user avatar
1 vote
0 answers
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confused by explanation of electromagnetic wave in physics textbook

I'm kind of confused by the proof used in my physics textbook to explain an electromagnetic field using Faraday's law. The text book uses Faraday's law to try to explain why a uniform electric field ...
Jerry Hsieh's user avatar
1 vote
0 answers
99 views

Do we need Killing vectors to have wave vectors in a plane wave solution?

It is well known, and there are other questions in this website that answer this, that one needs a stationary Killing vector field to judge if a plane wave has positive or negative frequency. If our ...
tonetillo 4's user avatar
1 vote
0 answers
41 views

Recovering planar wave from Huygens principle

I am trying to get a basic understanding of the Huygens principle, by checking whether a planar wave is the same as what is calculated from the principle when the wave reaches a screen. ...
Ziyuan's user avatar
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0 answers
88 views

What is Raleigh expansion?

I am currently reading the paper The dielectric lamellar diffraction grating, in which the electric field above and bellow a 1D grating (grooves) is expressed as a "series of outward-going plane ...
henry's user avatar
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1 answer
100 views

Confusion in the plane wave solution for the EM wave equation

When talking about the solution of the Wave Equation for the Electric Field: \begin{equation} \ddot{E}=c^2\nabla^2E \end{equation} One usually assumes a sinusoidal waveform and writes: \begin{equation}...
Adrien-Marie Deschamps's user avatar
2 votes
2 answers
800 views

Complex form for the Plane wave

It's a very well-known fact that plane waves can be represented in the complex form: \begin{equation} \mathbf{F}(\mathbf{x},t)=\mathbf{F}_0e^{i(kx-\omega t)} \end{equation} However, I've been ...
Johann Wagner's user avatar
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183 views

How to show momentum operator are plane waves using translation operator

Using the momentum operator $ \hat{p}\rightarrow-i\hbar\frac{d}{dx} $ and the translation operator $ e^{-i\hat{p}a/\hbar}\psi(x)=\psi(x-a) $, how to I go about showing that the eigenfunctions of the ...
Anne's user avatar
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0 votes
2 answers
284 views

Jefimenko's equations contradiction between free space solutions

In Jefimenko's equations, which are a solution to Maxwells equations. Each term has either $\rho $ or $J$ in it. Setting $\rho$ and J to be zero, Should reduce to the electromagnetic plane wave ...
jensen paull's user avatar
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0 answers
52 views

How can the particle in plane progressive harmonic wave have minimum potential energy at one of the extreme position?

consider this image context: These are fill in the blanks sort of questions, the above image contains solution. My reasoning A and B should be in SHM and we know that in SHM Kinetic Energy is max at ...
Rambal heart remo's user avatar
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0 answers
55 views

Plane waves vs continuous sine waves

I've started learning QFT from Sean Carroll's lectures, but I had to postpone it until I'll manage my notes)) Meanwhile, 1 question is bugging me: it's about 3D plane waves, which in QFT are analogous ...
Victor Novak's user avatar
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1 answer
141 views

What are the stokes parameters of a linear wave added to a circular one?

So consider the following thing: Let's suppose that we have a situation with two monochromatic waves propagating through the z-axis. Both waves have the same frequency and intensity. How can I find ...
kplt's user avatar
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0 answers
33 views

How can I prove this property about linearly polarized waves?

So I'm studying electromagnetic waves. The current topic is polarization. My professor material says in one part that the electric field of a monochromatic linearly polarized wave propagating through ...
kplt's user avatar
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0 answers
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A couple of apparent inconsistencies on free-particle stationary states

In order to introduce my question we consider first the free electron, in a box width L, with eigenfunctions and eingenvalues given by $$\psi_k(x)=\frac1{\sqrt{L}}e^{ikx}$$ and $$E_k=\hbar^2k^2/2m$$ ...
Francesco's user avatar
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0 answers
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Accounts on the solutions of the Dirac equation

Consider the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi = 0$. As it is well known, there are different representations for the matrices $\gamma^{\mu}$, $\mu = 0,1,2,3$, the most famous ones ...
MathMath's user avatar
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Plane waves solutions for Dirac equation in terms of eigenstates of helicity

Suppose $\sigma_{1},\sigma_{2}$ and $\sigma_{3}$ are the Pauli matrices. Given a momentum ${\bf{p}}$, we define the helicity operator: $$ h = \frac{1}{2}\begin{pmatrix} {\bf{\sigma}}\cdot {\bf{\hat{p}}...
MathMath's user avatar
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4 votes
1 answer
369 views

What is the graphical representation of a wave plane of the form $e^{i(\vec{k}.\vec{r}-\omega t)}$ or $e^{i(k.x-\omega t)}$?

Let's consider a plane wave of the form $e^{i(\vec{k}.\vec{r}-\omega t)}$ Is the graphical representation the following or the following ? I'm wondering what is now the graphical representation for ...
Mathieu Krisztian's user avatar
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1 answer
402 views

How and why the state of free particle in quantum physics is represented by plane wave packet? [closed]

In Quantum Mechanics (Cohen Tannoudji) Topic: "Asymptotic Form Of Stationary Scattering States" It is written that for large negative values of $t$, the incident particle is free and it's ...
Garry's user avatar
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2 votes
1 answer
1k views

What is the propagation direction of plane wave?

As far I know, plane wave equation is given by: $$\vec{E}(\vec{r},t)=\vec{E_0} \cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm} \tag{1}$$ In some textbook propagation direction of $(1)$ is ...
Suresh's user avatar
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1 answer
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Finding helicity eigenstates

Question: Give the mode expansion of the $A_i$ in terms of plane wave \begin{equation} \epsilon^{\pm}_i(p)e^{-ip \cdot x} \ \ \ \ \ \text{ and } \ \ \ \ \ \epsilon^{*\pm}_i(p)e^{-ip \cdot x} \...
user3397129's user avatar
16 votes
5 answers
4k views

Why do physicists use plane waves so much?

When looking at solutions of the Dirac equation people tend to give solutions as $$\psi^{(1)} = e^{\frac{-imc^2t}{\hbar}}\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix},\psi^{(2)} = e^{\frac{-imc^2t}{\hbar}}\...
Ryan Parikh's user avatar
0 votes
2 answers
282 views

What is meant by "a plane wave that has the periodicity of a Bravais lattice"?

I'm reading through Ashcroft & Mermin's chapter on reciprocal lattices and am confused about this sentence: Consider a set of points R constituting a Bravais lattice, and a plane wave, e^{i k*r}. ...
Mohanachz's user avatar
2 votes
1 answer
89 views

Modelling sky noise using a 2D array with plane waves

I have a question about modeling sky noise which should be filtered by a spatial filter 4f system. My approach for this task is to use a 2D array with random amplitude values and another 2D array that ...
Nabla94's user avatar
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1 vote
3 answers
69 views

Why spacetime translations don't affect the physics of de Broglie plane waves?

I'm studying Merzbacher's Quantum Mechanics. In Chapter 2 Section 1, he "derives" the expression $\psi(x, t)=Ae^{i(kx-\omega t)}$ for the de Broglie plane waves for free particles. Basically ...
Atom's user avatar
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0 votes
2 answers
454 views

Why is zero conductivity media called lossless?

Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
Shardul Maurya's user avatar
1 vote
1 answer
605 views

Plane Wave Decomposition of Electric Field

I've tried to understand the decomposition of an HF electrical field in a series of plane waves. $$\vec{E}(\vec{r}, t) = \int\int\int \hat{\vec{E}}(\vec{k}) \cdot\mathrm{e}^{\mathrm{i}(\vec{k}.\vec{r}-...
ElektroTransformator's user avatar
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3 answers
842 views

What Plane Waves Make a Gaussian Beam?

When I think of a light beam, what first comes to mind is this: Black lines are axes (both spatial axes, at a snapshot in time), and blue lines represent the surfaces of constant phase of a plane ...
flevinBombastus's user avatar
0 votes
1 answer
417 views

Determining plane wave polarization given the magnetic-field vector phasor

Given the following magnetic-field vector phasor: $$\vec H(\vec r)=\left[\hat x - j\hat y\right]H_o e^{jkz}$$ I need to find the associated E-field vector phasor so that I can determine the ...
Landon's user avatar
  • 189
1 vote
4 answers
344 views

Few doubts in the solutions of step potential in Quantum mechanics [closed]

Assume we have a step potential $$ V(x)=\left\{\begin{array}{ll} 0, & x<0 \\ V_{0}, & x \geq 0 \end{array}\right. $$ and we fire particles from a distance $s$ towards the barrier from the ...
Kashmiri's user avatar
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