Hello,
I hope I got the section right ;). I orginally posted this in the physics section, but as the problem is more mathematical. It would be nice if someone knows the right direction.
I've stumbled upon a math problem while going through some physics and got stuck with some mathematical...
Hello,
I'm currently going through Agrawal's book 'Nonlinear Fiber Optics' and got stuck with some mathematical cosmetics (pp. 40). It is the substition of:
\vec{P_L}(\vec{r},t) = \frac{1}{2} \hat{x} \left(P_L \exp{(-i \omega_0 t)} + c.c.\right)
into
\vec{P_L}(\vec{r},t) = \epsilon_0...
I wanted to prove the periodicity in x. All the resources I've found so far always used these handwaving arguments. But I wanted to see it coherently on paper why the proof works like that. Starting with that I stumbled on some problems.
w + u^{inc} = 0 was a mere try to somehow get...
True that solves it. Thank you alot. I was wondering though: in general it holds that
n \times (H_1 - H_2)
Why does this not work here and just leads to the Dirichlet boundary conditions once again?
Is the following logic sound to finally prove pseudo-periodicity:
due to uniqueness...
Thank you andy.
For the first part I agree:
(n1, n2, 0) x (0,0,u) = (n2 u, -n1 u, 0) = 0.
This directly implies that u = 0.
But to get the boundary condition for TM, I don't see it. Without applying any other equation you directly get the same boundary condition as before, as now H =...
Hi
for my thesis I wanted to show the complete derivation for the grating equation - case: perfectly conducting. The later steps are all no problem, but I am struggling with the proof of pseudo-periodicity. I found in my opinion a nice summary here...
Stevendaryl and tom.stoer! Thank you very much for your replies. I think I got it finally, one question that directly follows: is it then right to say that:
<M> = \Sigma p(m|i)m
and hence M = \Sigma P_m m
Shouldn't the density matrix be 4x4? The first one should be something like
\begin{pmatrix}
1 & 0 & 0 & 1\\
0 & 0 & 0 & 0\\
0 & 0 & 0 & 0\\
1 & 0 & 0 & 1
\end{pmatrix}
The others then analogously, but a 100% I am not certain, because looking at the Schmidt-coefficients, they are...
Hi Folks,
I somehow cannot get the difference and have to admit that I am left confused.
For a probability of measuring m with the operator M on state \Psi_i
p(m|i) = <\Psi_i| M^{+}_m M_m |\Psi_i> = <\Psi_i| M_m |\Psi_i>.
The average of an observable is defined as <O> = <\Psi_i| O...
Sorry for this very late reply. First of all: thank you very much for your answer. Yes, I was talking about EM-waves. More about a pulse in the visible region though. I wondered how one would then discriminate and measure phase and group velocity. Using a phase detector sounds reasonable, but...
Thank you very much. I think I spotted the problem with the matrix, as for square-matrices the Moore-Penrose inverse needs independent vectors, but unfortunately there is two dependent column vectors. At first sight I just spotted degenerate row vectors, but of course there has to be dependent...
hmm..what do you mean by that least square approach? I just wanted to check a solution, I just don't understand the mathematical reason why the last system cannot be solved for A00, B00 and C00.
How would you go about the least square approach though?
Hi chiro,
thank you very much for your reply. Yes I am using the Moore-Penrose pseudo-inverse. Actually the original problem can be seen in the attached picture. After using the pseudo-inverses it is stated that only the first three systems have a solution, but that there is too little...
Dear fellows,
during my internship I've stumbled over a problem of analysis. To cut things short some pseudoinverses have to be calculated. For one of them it does not work, s.t. A'*A \neq I.
I just wondered about the requirements to find a pseudoinverse. One of the eigenvalues is zero...
Hey folks,
some weeks ago we had an trial-exam and one of the questions there was: "How do you measure phase and group velocity."
That question really got me. Having a fastly oscillating wave as carrier and then the envelope. Can someone help me? Is it impossible for the phase, as it is...
Dear fellow physicists,
looking at the derivation for the maxwell equations into k-space, I've stumbled upon something that seems not so logical to me. It is concerning the two parts where they transform \nabla \times E and \nabla \bullet E on page 27 (on the sheets 14)...
Hello,
whenever I come to the derivation of the Fresnel equations I get stuck on the boundary condition for the component of the E-Field that is parallel to the surface.
I know for the parallel components Maxwell dictates that:
E_{1t} = E_{2t}.
For the parallel incoming light field...
Thank you very much Born2bwire! Now I also get: ∫(∇2G)e−ikxdV=∫(∇G)e−ikxdS−∫∇G∇e−ikxV.
That makes sense now, but when I apply the 'integration-by-parts' again on the last term, I have a slight problem because the divergence theorem..well is working with divergences, but here we have a grad...
Hey all,
some weeks ago in a tutorial our TA solved Poissons equation with Greens functions..would be very short, but he also derived the Greens function using a Fourier transform. Two points I really don't get and he could also not explain it. Maybe you can help me? There might be even a short...