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Why doesn't the expectation of position for a plane wave obey kinematics?

Consider the plane wave: $$\Psi = Ne^{i(\vec{p}\cdot\vec{r} - Et)/\hbar}$$ with N is the normalisation factor. The expectation value of momentum for this wave is: $$\begin{align} ...
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1answer
43 views

Uniform Plane Question [closed]

Question: Communicating with submarines is very challenging due to the fact that seawater is a conductor (conductivity of roughly 5 S/m). This conductivity indicates that electromagnetic waves do not ...
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1answer
20 views

Pulsed plane wave

My question is specifically concerned with ultrashort pulses: can a plane wave (one with infinite spatial extension) have a finite duration in time? Is there some physical principle that is violated ...
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0answers
36 views

Plane-wave wave function in 3D with vector potential

I was looking into a monopole scattering problem in 3D with magnetic potential. What would be the most general incident plane wave solution ? The way I see this is that I need to ensure that current ...
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1answer
28 views

How can pressure and velocity fluctuations in acoustic plane waves be in phase and still hold to the B.C. that velocity must be zero at a solid wall?

In linear plane-wave acoustics (no mean flow, small perturbations, etc.), it is often derived that the phase of a traveling pressure fluctuation wave and a fluctuation velocity wave are the same. For ...
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1answer
68 views

Poyting theorem for a plane wave

I would like to apply and verify the Poynting theorem for a uniform plane wave but there is obviously something wrong in my demonstration. The Poynting theorem expresses the conservation of energy: ...
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0answers
41 views

Electric field operator in 2D geomatry

In the free field (3D), transverse electric field operator is given by the below expression; $$e^{\bot}(\textbf{R}) =i \sum_{\textbf{p},\lambda}\Big( \frac{\hbar cp}{2V\epsilon_{0}}\Big)^{1/2} ...
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0answers
45 views

Plane wave conditions

Which conditions have to be fulfilled in order to approximate a light beam by a plane wave (i.e. $\phi(x)\approx \phi(0)e^{ikx}$)? I am looking for both mathematical and experimental conditions. At ...
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1answer
298 views

Understanding wave packets, in particular matter waves, dispersion and point particles

Here is what I have gathered so far: Particles like an electron (i.e. with rest mass) can be represented as matter waves (deBroglie). The matter wave of a particle can be modelled a wave packet. A ...
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3answers
355 views

The ubiquitous Planewave Ansatz

In physics, the planewave ansatz (meaning: an educated solution guess) is very ubiquitously used, when solving differential equations, in different domains of physics. E.g. to solve the dispersion ...
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2answers
87 views

Importance of the $\exp (i \bar{k} \cdot \bar{r})$ part of the plane wave equation

I am having trouble grasping how the equation $\bar{E} \left( \bar{r}, t \right) = \bar{E}_{0} \exp \left[ i \left( \bar{k} \cdot \bar{r} - \omega t \right) \right]$ fully describes a plane wave. ...
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Why are EM waves transverse?

I was reading Griffiths' Introduction to Electrodynamics, specifically the section on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to ...
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2answers
91 views

Trouble understanding phase matching equation

consider a 2nd order non linear optical material, i.e. a material in which it holds that $ P = \epsilon_0 E + 2dE^2$. In the Born approximation, the non linear contribution to the polarization density ...
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2answers
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How to find the amplitude of magnetic field of this plane wave

Because my previous question was short and confusing, it was put on hold. This is my new question, which getes straight to the point. I have an electromagnetic plane wave which has wavelength $λ$ = ...
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2answers
171 views

Can the wave function of the hydrogen atom be written as a superposition of plane waves with a single frequency?

The solutions of the Schrödinger equation for a hydrogen atom have definite energy. Does this mean that they could be written as a superposition of plane waves of a single frequency - corresponding to ...
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0answers
89 views

Rewriting $\langle {\bf k} \vert E,l,m \rangle$ as $\langle {\bf k} \vert ~k,l,m \rangle$ Spherical Harmonics

From Sakurai eq. 6.4.21a we have that $$\langle {\bf k} \vert E,l,m \rangle=\frac{\hbar}{\sqrt{M k}}\delta\left(E-\frac{\hbar^2 k^2 }{2M}\right) Y_l^m({\bf\hat k}),$$ where $M$ is the mass of the ...
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1answer
52 views

What does this term G+G'->G' mean?

In this document, what does the line "Write $\vec{G}_i + \vec{G}_i' \rightarrow \vec{G}_i'$" after equation (25) actually mean?
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0answers
61 views

Conceptual way of understanding what material 'does' at critical angle

I would like a conceptual way of understanding how a material behaves at the critical angle. So why does it all reflect? I can see why it reflects in the maths, but conceptually, it doesn't make ...
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1answer
1k views

Definition of complex permittivity

I'm not sure if this is the appropriate forum for my question as I actually am studying this as part of electrical engineering and I don't actually study physics. Nonetheless, I shall ask and if need ...
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3answers
3k views

Why is there a 90˚ phase angle between particle velocity and sound pressure in spherical waves?

My text says that in a plane sound wave (or in the far field), particle velocity and pressure is in phase. As we move closer to the sound source (to near field and more spherical waves), the phase ...
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2answers
862 views

Why is Polarization of a wave important, and what happens when a wave is polarized in all three dimensions?

I don't quite understand this, I understand that given a wave traveling in a certain direction, it will be polarized in the direction its not travelling in, so if its travelling in the Z direction, k ...
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0answers
630 views

Hankel function in terms of planewaves [closed]

It is well know that planewaves are a complete basis for solutions to the wave equation. Let us assume a 2D space, and at fixed temporal frequency, the equation reduces to the Helmholtz equation. In ...
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4answers
588 views

Are electromagnetic “plane” waves measurable or just a virtual concept?

I find plane waves are uncompatible with light cone. Perhaps plane waves are "virtual" and can never be measured in that case, shouldn't we call plane waves as "virtual plane waves"? (other option ...
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4answers
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Popular depictions of electromagnetic wave: is there an error?

Here are some depictions of electromagnetic wave, similar to the depictions in other places: Isn't there an error? It is logical to presume that the electric field should have maximum when ...
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0answers
71 views

Reorienting a sensor axes according to particle displacement directions

Consider a sensor which is located inside the solid substance. This sensor is capable of detecting the substance oscillations along each of the three axes (usually orthogonal, but generally, any ...
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1answer
218 views

Reflected and refracted wave sphased

When we derive refraction and reflection laws for a generical plane wave on a surface, we say that reflected and refracted must be in phase with the incident wave. Why a medium cannot do a sphased ...
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2answers
307 views

Notation of plane waves

Consider a monochromatic plane wave (I am using bold to represent vectors) $$ \mathbf{E}(\mathbf{r},t) = \mathbf{E}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}, $$ $$ ...