Recent content by lholmes135

I think I figured it out. Because the electric field is polarized in the x direction and the magnetic field in the z direction, I can just use the x component of permittivity and the z component of the magnetic field, so in this problem ##\lambda=\lambda_0## in both cases.

Sure. ##\lambda=\frac{\lambda_0}{\sqrt{\epsilon_r\mu_r}}##, so in your example the wavelength would be half of that as in free space. The problem in anisotropic materials is that when ##\epsilon## and ##\mu## are tensors, I don't know what values to use.

Calculate the wavelength for an ##E_x## polarized wave traveling through an anisotropic material with ##\overline{\overline{\epsilon}}=\epsilon_0diag({0.5, 2, 1})\text{ and }\overline{\overline{\mu}}=2\mu_0## in: a. the y direction b. the z direction Leave answers in terms of the free space...

For calculating D it makes sense, but there are many other equations where it seems strange to use a tensor. How about for calculating the index of refraction? ##n=\sqrt{\epsilon_r\mu_r}##. Since ##\epsilon## and ##\mu## depend on the direction of the electromagnetic wave and its polarization...

I should have specified, I am talking about in an electromagnetic wave.

If I have an anisotropic material with permittivity: $$\epsilon= \begin{pmatrix} \epsilon_{ii} & \epsilon_{ij} & \epsilon_{ik} \\ \epsilon_{ji} & \epsilon_{jj} & \epsilon_{jk} \\ \epsilon_{ki} & \epsilon_{kj} & \epsilon_{kk} \\ \end{pmatrix} $$ What exactly does each element represent in this...

This is what I was looking for, thanks.

In the attached image, there are two quantum circuits that are equivalent. I am trying to understand how. Let's call the top qubit ##q_1## and the bottom one ##q_2##, and the outputs ##q_1'## and ##q_2'##. From what I understand, the C-NOT gate doesn't affect the control qubit. Because Hadamard...

I think I have an explanation without the Stirling approximation. $$ \lim_{n \rightarrow +\infty} { \frac {N!} {(N-n)!N^n} } $$ $$ \lim_{n \rightarrow +\infty} { \frac {N*(N-1)*...*(N-n+1)} {N*N*...*N} } $$ There are n terms in both the numerator and denominator, so this can be written as $$...

I suppose I should add some context. This isn't homework. My textbook is deriving a certain formula and I'm trying to follow the derivation. At one step they say something like "and obviously we can use the Stirling formula to show that ..." and show the equation in question. Mathman has posted...

Thanks Mark, good catch. So fixing the signs and using the same N-n = N approximation we have: $$ \lim_{N \rightarrow +\infty} {[Nln(N)-N]} - \lim_{N \rightarrow +\infty} {[(N-n)ln(N-n) - (N-n)]} - n \lim_{N \rightarrow +\infty} {ln(N)} $$ $$ \lim_{N \rightarrow +\infty} {[Nln(N)-N]} -...

I'm trying to determine why $$ \lim_{N \rightarrow +\infty} ln( \frac {N!} {(N-n)! N^n}) = 0$$ N and n are both positive integers, and n is smaller than N. I want to use Stirling's, which becomes exact as N->inf: $$ ln(N!) \approx Nln(N)-N $$ And take it term by term: $$ \lim_{N...