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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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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 ...
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1answer
43 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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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
169 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
1k 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
419 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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371 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
444 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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3answers
1k 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 ...
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0answers
66 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
140 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
265 views

Notation of plane waves

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