Questions tagged [plane-wave]
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83
questions
0
votes
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}
\...
13
votes
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 $$\psi^{(1)} = e^{\frac{-imc^2t}{\hbar}}\begin{pmatrix}1\\0\\0\\0\\\end{pmatrix},\psi^{(2)} = e^{\frac{-imc^2t}{\hbar}}\...
2
votes
1answer
58 views
Modelling sky noise using a 2D array with plane waves
I have a question about modeling sky noise which should be filtered by a spatial filter 4f system. My approach for this task is to use a 2D array with random amplitude values and another 2D array that ...
1
vote
3answers
54 views
Why spacetime translations don't affect the physics of de Broglie plane waves?
I'm studying Merzbacher's Quantum Mechanics. In Chapter 2 Section 1, he "derives" the expression $\psi(x, t)=Ae^{i(kx-\omega t)}$ for the de Broglie plane waves for free particles. Basically ...
0
votes
0answers
18 views
X-Ray Diffraction: Calculate the phase difference at the detector between waves scattered by 2 different points in a sample
I have very little idea what I'm doing here, but my goal is to calculate the difference in phase of the waves scattered by 2 points in some sample. The figure below shows my interpretation of the ...
0
votes
2answers
28 views
Why is zero conductivity media called lossless?
Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
0
votes
0answers
17 views
Interference of Plane Waves At an Angle in a Moving Reference Frame
Suppose I have two plane waves: one propagating along $z$ and the other propagating at an angle $\theta$ in the $x-y$ plane with respect to the $z$ axis. That is, $k_1 = k_0 \hat{z}$ and $k_2 = k_0(\...
1
vote
1answer
55 views
Plane Wave Decomposition of Electric Field
I've tried to understand the decomposition of an HF electrical field in a series of plane waves.
$$\vec{E}(\vec{r}, t) = \int\int\int \hat{\vec{E}}(\vec{k}) \cdot\mathrm{e}^{\mathrm{i}(\vec{k}.\vec{r}-...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
2
votes
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 ...
0
votes
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 $\omega$ ...
0
votes
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 ...
1
vote
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^{...
0
votes
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 ...
1
vote
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 ...
0
votes
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:...
0
votes
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 ...
3
votes
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 ...
0
votes
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 ...
0
votes
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
$$ \vec E(\...
2
votes
1answer
53 views
Acoustics: Construction of the pressure field with transmitted and reflected plane waves
So I have been reading one of the papers about wave manipulation, which takes advantage of the phase shifted reflection by tailoring the design of the system. The design has two domains: air and foam (...
0
votes
1answer
61 views
Glint effect in electromagnetic waves [closed]
Two plane waves having the same frequency and different intensities:
$$E_0=Ae^{i(\omega t-kr_0)}$$ and
$$E_1=Be^{i(\omega t-kr_1)}$$
arrive at point $P=(x,y)$ from two point sources located at a ...
1
vote
2answers
39 views
Turning angles in Radio and Telephone [closed]
Radio waves and microwaves are usually plane polarised. This is why you can sometimes get a better signal if you turn a radio or telephone through different angles.Okay what happens when we turn a ...
3
votes
2answers
362 views
What does the spherical-harmonic notation $Y^{m}_l(\hat{\textbf{r}})$ mean, and how does it relate to the usual $Y^m_l(\theta, \varphi)$?
By using the plane wave expansion, the decomposition of stationary harmonic plane wave into partial waves can be given by
$$
e^{i\textbf{k}\cdot\textbf{r}} = e^{ikz} = e^{ikr\cos\theta} = \sum^{\infty}...
1
vote
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
$p_z - \gamma$
...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
2
votes
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 $(...
0
votes
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 $...
0
votes
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\...
0
votes
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(...
1
vote
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 ...
2
votes
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
0
votes
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 ...
1
vote
0answers
96 views
Null reflection coefficient in oblique incidence
A plane wave traveling in free space has an electric field phasor of
$$
\textbf{E}(x,y,z) = E_{0}^{+}( \textbf{u}_{x} - \textbf{u}_{y} + \textbf{u}_{z})\cdot e^{-jk_{0}(x\sin \theta + z \cos \theta)}
...
15
votes
3answers
2k views
What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?
I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form
$$f(x) ...
6
votes
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
votes
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 ...
1
vote
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
$$A(z,t) = \int_{\...
1
vote
1answer
137 views
Solution of Dirac equation: arbitrary polarizations
In my lecture notes (signature $-+++$) we find the free Dirac equation solutions. We proceed in this way:
Dirac equation:
$$
(i\,\displaystyle{\not} p +m)\psi(x) = 0
$$
We make the following ansatz:...
-1
votes
2answers
36 views
What is the simplest way to see that this abstract plane wave is “traveling” at the speed of light?
In EMFT notation,
$$
{\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
$$
I am having trouble ...
0
votes
2answers
331 views
Electromagnetic fields in a cubical cavity
I'm trying to solve the standing electromagnetic modes in a cubical cavity problem without using separation of variables. The cube is a perfect conductor, and hence the boundary conditions are $E_{\...
1
vote
1answer
204 views
Non-plane wave solutions to Dirac equation?
Solutions to Dirac equation
$$(-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\...
