Questions tagged [plane-wave]

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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 $a$, ...
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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 ...
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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, ...
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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 ...
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Diffraction of a plane wave

Let's consider a plane wave hitting a surface with an aperture of width e in the following fashion: The amplitude of the plane wave is given by: $ a({\bf r})=a_0\exp(i{\mathbf k}\cdot{\mathbf r}) $ ...
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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 ...
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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.
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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 ...
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Non-physical plane wave states in infinite domain

My question regards Appendix A in Rubin H. Landau's A Second Course in Quantum Theory. I do not see what he means when he says $\Delta i\equiv 1$ (below). In fact, I think the infinite domain is ...
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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 ...
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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. ...
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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 ...
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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}...
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2 answers
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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 ...
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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 ...
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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 ...
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Magnetic field of a standing monochromatic plane wave

I am given the magnetic field of a standing monochromatic plane wave $$\vec{H}(y,t)=H_0\sin(\beta y+\theta_0)\sin(\omega t+\phi_0)\,\hat e_x$$ and i am asked to determine in what type of medium its ...
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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 ...
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Optical path difference between the first and p-th transmitted wave for a plane wave incident on a Fizeau interferential wedge

In this paper: Ayerden, N. P., Graaf, G. D., & Wolffenbuttel, R. F. (2016). Compact gas cell integrated with a linear variable optical filter. Optics Express, 24(3), 2981-3002. https://doi.org/10....
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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 ...
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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 ...
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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 ...
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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 $$E_k=\hbar^2k^2/2m$$ ...
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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 ...
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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}}...
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3 votes
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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 ...
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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 ...
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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 ...
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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} \...
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5 answers
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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}}\...
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2 votes
1 answer
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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 ...
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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 ...
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Why is zero conductivity media called lossless?

Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
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1 answer
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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}-...
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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 ...
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1 answer
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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 ...
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1 vote
4 answers
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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 ...
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2 votes
2 answers
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Why is the plane wave ansatz appropriate for scattering cross sections of a localized particle beam?

This question is a spin-off from this related question: Why does the Born approximation for the scattering amplitude depend on the potential $V$ everywhere in space, unlike classical scattering? This ...
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1 answer
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Normalization for a free Dirac plane wave

I've recently come about the free plane wave solutions to the Dirac equation, and i'm having a hard time proving that the normalization factor $n$ is $$n=\frac{1}{\sqrt{2m(m+\omega)}}$$ Where $\omega$ ...
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1 vote
1 answer
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Basis for F. Mandl's interpretation of the amplitude of a plane wave

I'm going through Mandl's Quantum Mechanics and I'm having trouble understanding some of the moves he makes when discussing the finite potential barrier. He begins by interpreting the plane wave $Ae^{...
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1 answer
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electronic band structure calculation using plane wave expansion: what are the diagonal matrix elements for a coulomb potential?

I'm trying to do a plane wave basis expansion calculation for the band structure / wavefunctions of electrons in a periodic solid, using a coulomb potential for the nuclei. I'm working from Ashcroft ...
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Snells Law derivation from Plane Wave incidence

I am trying to derive snell's law from plane wave incidence by imposing the condition that the phase of the incident, reflected and transmitted wave at the point of incidence must be equal. Here's ...
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How to determine wave vector given the polarization of a plane wave

This is very similar to the question asked in the past, but I need further clarification. Say I'm given the polarization of an electromagnetic wave in free space (in phasor form), something like this:...
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Acoustic Plane Wave

Consider an ideal fluid which we have a spherical object on it and a progressive plane wave is heading the object. I have a simple question and it is: If we assume the amplitude of the incident ...
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3 votes
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Rigorous plane wave expansion in QFT

I work with quantum field theory in curved spacetimes, so I'm not fully aware of the notation used in standard QFT. However, I'll try to make myself clear. In standard QFT, the one-particle Hilbert ...
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1 answer
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Behaviour at an interface plane wave

I have this example diagram that was given in one of my lectures and I am just going through what the equation given actually mean and calculating some results from the equation. Which are the angle ...
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1 answer
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Why is the electric field phase shifted in this circular plane wave?

The $x$-component of a circular polarized plane wave is $$ E_x(\vec r,t)=E_0\cos\left(\frac{w}{c}(0.6y-0.8z)-wt\right) $$ With only this given, we can devise the total electric field as $$ \vec E(\...
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2 votes
1 answer
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Acoustics: Construction of the pressure field with transmitted and reflected plane waves

So I have been reading one of the papers about wave manipulation, which takes advantage of the phase shifted reflection by tailoring the design of the system. The design has two domains: air and foam (...
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1 answer
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Glint effect in electromagnetic waves [closed]

Two plane waves having the same frequency and different intensities: $$E_0=Ae^{i(\omega t-kr_0)}$$ and $$E_1=Be^{i(\omega t-kr_1)}$$ arrive at point $P=(x,y)$ from two point sources located at a ...
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1 vote
2 answers
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Turning angles in Radio and Telephone [closed]

Radio waves and microwaves are usually plane polarised. This is why you can sometimes get a better signal if you turn a radio or telephone through different angles.Okay what happens when we turn a ...
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