Questions tagged [plane-wave]

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1answer
41 views

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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5answers
3k 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}}\...
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1answer
58 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 ...
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3answers
54 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 ...
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0answers
18 views

X-Ray Diffraction: Calculate the phase difference at the detector between waves scattered by 2 different points in a sample

I have very little idea what I'm doing here, but my goal is to calculate the difference in phase of the waves scattered by 2 points in some sample. The figure below shows my interpretation of the ...
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2answers
28 views

Why is zero conductivity media called lossless?

Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
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0answers
17 views

Interference of Plane Waves At an Angle in a Moving Reference Frame

Suppose I have two plane waves: one propagating along $z$ and the other propagating at an angle $\theta$ in the $x-y$ plane with respect to the $z$ axis. That is, $k_1 = k_0 \hat{z}$ and $k_2 = k_0(\...
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1answer
55 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}-...
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3answers
49 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 ...
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0answers
26 views

Superposition and Boundary Conditions in Standing Waves

A standing wave is formed due to superposition of two waves with same anplitude, wavelength and period but propagating towards opposite direction to each other. I would like to focus on how initially ...
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1answer
34 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 ...
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4answers
97 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 ...
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2answers
34 views

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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1answer
134 views

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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0answers
18 views

Number of Augmented plane waves(APWs) needed to describe a unit cell

I am a beginner at learning Density Functional theory. My question is, while evaluating augmented plane wave basis(or LAPW)numerically,how are the number of plane wavefunctions needed for a particular ...
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1answer
28 views

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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1answer
117 views

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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0answers
42 views

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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2answers
39 views

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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0answers
37 views

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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0answers
138 views

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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1answer
51 views

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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1answer
53 views

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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1answer
53 views

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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1answer
61 views

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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2answers
39 views

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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2answers
362 views

What does the spherical-harmonic notation $Y^{m}_l(\hat{\textbf{r}})$ mean, and how does it relate to the usual $Y^m_l(\theta, \varphi)$?

By using the plane wave expansion, the decomposition of stationary harmonic plane wave into partial waves can be given by $$ e^{i\textbf{k}\cdot\textbf{r}} = e^{ikz} = e^{ikr\cos\theta} = \sum^{\infty}...
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0answers
30 views

Conservation law charge in plane-wave

When considering a charged particle in a plane-wave field, it is possible to show that the 2 following quantities are conserved $\boldsymbol{p}_{\perp} - e\boldsymbol{A}_{\perp}$ and $p_z - \gamma$ ...
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3answers
333 views

Plane wave and polarisation

I am trying to understand the concept of a polarisation of a plane wave. Generally, the plane wave can be seen as a sum of two orthogonal linearly polarized waves. according to Wikipedia. So I have ...
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0answers
34 views

What is the load reflection coefficient for a uniform plane wave travelling at the boundary between a dielectric and a perfect conductor?

Suppose you have a uniform plane wave travelling from a dielectric medium towards a perfect conductor (suppose the interface is planar as well). From my understading of the theory behind EM waves and ...
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1answer
44 views

Plane wave propagation constants being equal across all components

Starting from the wave equation for electric field in free-space, $$ \nabla^{2}\boldsymbol{E}+k^{2}_{0}\boldsymbol{E}=0, $$ where $k_{0}$ is the free-space wavenumber, we usually proceed in deriving ...
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2answers
69 views

Oscillations of plane waves

I am reading this notes on electromagnetism. On page 25 it reads the following, about planes waves: A plane wave propagating in the direction of z has no oscillations in the transverse plane $(...
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1answer
173 views

Function expansion in terms of plane waves

I would like to expand a function $f(r)$ in terms of plane waves of the form $e^{ikr}$. With expansion coefficients $f_k$, one can write $$ f(r) = \sum_kf_k e^{ikr}. $$ Now I need the coefficients $...
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1answer
452 views

The curl of phasor of electric field

Let the phasor electric field of a uniform plane wave be $\vec{E_{0}}e^{-i\vec{k} .\vec{r}}$ where $\vec{k}$ is the wavenumber vector and $\vec{r}$ the position vector. why is then, $\frac{1}{-i\...
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1answer
2k views

What is the Fourier transform of an infinite integral of plane waves?

I'm trying to evaluate this double-integral in the context of Quantum Mechanics. Consider $f(x)$ as $$ f(x) = \int_{-\infty}^{\infty} \mathrm{exp} \left( \frac{-ipx}{\hbar} \right) dp $$ So $\hat f(...
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1answer
647 views

What is the logic behind box normalization and periodic boundary condition?

Free particle energy eigenfunctions are $A\exp{[i(Et-\textbf{p}\cdot\textbf{r})/\hbar]}$ are non-normalizable. To normalize them one introduces a procedure called 'box normalization' where one imposes ...
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2answers
463 views

Proof of non-orthogonality E and H fields of an electromagnetic wave in certain materials?

I understand that electromagnetic waves must have orthogonal E and H fields in free space from Maxwell's third equation. However, I saw on a Quora post that these fields do not necessarily have to be ...
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1answer
836 views

Is a plane wave necessarily monochromatic?

Is the expression $$\psi(x,t)=A\exp{i(kx-\omega t)}, \hspace{0.3cm}A=\rm constant$$ the most general form of the plane wave? If yes, does it mean that a plane wave is necessarily monochromatic? If ...
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2answers
131 views

What are plane waves in Bethe ansatz

I study Bethe ansatz, although my background is mathematics not physics. Can somebody explain to me what is plane waves? I have seen in many papers this expression that "The idea of the Bethe ansatz ...
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0answers
416 views

Wave packets and the uncertainty principle

In my lecture course, I am told that a wave packet $\varphi$ is a superposition of plane waves such that $$\varphi = \int a(k) e^{ik-iw(k)t} dk$$ The function $a(k)$ is then linked to probability and ...
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1answer
104 views

Magnetic field of a plane wave hitting a conducting surface

If the $E$ component of a plane monochromatic wave does not penetrate the conducting surface, what happens to the $B$ component? The $E$ field gets reflected back because we are talking about a ...
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0answers
96 views

Null reflection coefficient in oblique incidence

A plane wave traveling in free space has an electric field phasor of $$ \textbf{E}(x,y,z) = E_{0}^{+}( \textbf{u}_{x} - \textbf{u}_{y} + \textbf{u}_{z})\cdot e^{-jk_{0}(x\sin \theta + z \cos \theta)} ...
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3answers
2k views

What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?

I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form $$f(x) ...
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3answers
18k views

Sinusoidal to complex form of wave equation

I know that a sinusoidal plane wave can be represented by the wave equation $$ \psi (x,t)=A\, \cos(kx-\omega t) $$ I have also seen that a plane wave can be represented in complex exponential form as $...
6
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2answers
434 views

Understanding the wave equation in 3dimensions

I am learning about waves and the wave equation in lectures, and there was something interesting my lecturer said which I have not been able to find about online or in a book. With regards to the ...
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2answers
207 views

Wave packet expression

Speaking in general about plane waves propagating along $z$ (electro-magnetic waves, for example; not necessarily particles represented as waves), a wave packet can be defined as $$A(z,t) = \int_{\...
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1answer
137 views

Solution of Dirac equation: arbitrary polarizations

In my lecture notes (signature $-+++$) we find the free Dirac equation solutions. We proceed in this way: Dirac equation: $$ (i\,\displaystyle{\not} p +m)\psi(x) = 0 $$ We make the following ansatz:...
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2answers
36 views

What is the simplest way to see that this abstract plane wave is “traveling” at the speed of light?

In EMFT notation, $$ {\bf E} = E_0 \sin(\omega (t - \sqrt{\epsilon_0 \mu_0} z)) \hat{{\bf a}}_x \\ {\bf H} = H_0 \sin(\omega (t - \sqrt{\epsilon_0 \mu_0} z)) \hat{{\bf a}}_y $$ I am having trouble ...
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2answers
331 views

Electromagnetic fields in a cubical cavity

I'm trying to solve the standing electromagnetic modes in a cubical cavity problem without using separation of variables. The cube is a perfect conductor, and hence the boundary conditions are $E_{\...
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1answer
204 views

Non-plane wave solutions to Dirac equation?

Solutions to Dirac equation $$(-i\gamma^\mu\partial_\mu+m)\psi=0$$ are usually obtained by acting from the left with complex conjugate Dirac operator $$(i\gamma^\mu\partial_\mu+m)(-i\gamma^\mu\...