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7
votes
2answers
465 views

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 ...
0
votes
1answer
40 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 ...
0
votes
2answers
61 views

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 $λ$ = ...
2
votes
2answers
97 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 ...
1
vote
0answers
78 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 ...
0
votes
0answers
39 views

The orthonormality conditions for plane waves

The notes I'm using for QFT give an orthonormality condition for the following plane wave: \begin{align*} u_{r,k}(x) = \frac{1}{\sqrt{V}} \varepsilon_r(\mathbf{k})e^{ik \cdot x} \end{align*} (where ...
0
votes
1answer
48 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?
1
vote
0answers
50 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 ...
1
vote
1answer
254 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 ...
4
votes
3answers
2k 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 ...
0
votes
2answers
506 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 ...
4
votes
0answers
424 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 ...
1
vote
4answers
467 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 ...
12
votes
3answers
2k views

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 ...
1
vote
0answers
67 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 ...
2
votes
1answer
152 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 ...
1
vote
2answers
284 views

Notation of plane waves

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