Recent content by Observer Two

Homework Statement On Wikipedia there is an article about perturbation theory. To understand something I need to understand the following relation. They say: Homework Equations H |n> = E_n |n> So: <n| H = <n| E_n H is Hermitian. So: Why is this? The Attempt at a Solution...

Huh? I'm really missing something here. |z|^2 = z z^* So if in my case z = e^{\frac{-|t|}{t_c}} then z^* = e^{\frac{|t|}{t_c}} Or not?

Homework Statement I have the complex term g(t) = e^{\frac{-|t|}{t_c}} which is the degree of the coherence. Homework Equations Now I want to verify that: t_c = \int_{-\infty}^\infty \! |g(t)|^2 \, dt The Attempt at a Solution \int_{-\infty}^\infty \! |g(t)|^2 \, dt =...

Homework Statement I want to varify that the components of a homogenous electric field in spherical coordinates \vec{E} = E_r \vec{e}_r + E_{\theta} \vec{e}_{\theta} + E_{\varphi} \vec{e}_{\varphi} are given via: E_r = - \sum\limits_{l=0}^\infty (l+1) [a_{l+1}r^l P_{l+1}(cos \theta) - b_l...

Ughy. You are right. I looked it up again and it's not actually x^2 as in "position operator squared" but X^2 = x^2 + y^2 + z^2. I didn't sleep for 29 hours now, working for some exams. I'm slightly confused. My bad. Next time I'll use the exact template. :redface:

I'm doing something horribly wrong in something that should be very easy. I want to show that: [L^2, x^2] = 0 So: [L^2, x x] = [L^2, x] x + x [L^2, x] L^2 = L_x^2 + L_y^2 + L_z^2 Therefore: [L^2, x] = [L_x^2 + L_y^2 + L_z^2, x] = [L_x^2, x] + [L_y^2, x] + [L_z^2, x] = L_y [L_y...

I have been told this before but I don't see how this helps me to be honest. ∑q^x = \frac{1 - q^{n+1}}{1 - q} I'm surely overlooking something ... How do I apply this to my exp function?

\sum\limits_{m=-N}^N e^{-i m c} = \frac{sin[0.5(2N+1) c]}{sin[0.5 c]} I have to show the equality. But I'm absolutely dumbfounded how to even begin. I always hated series. I tried to use Euler's identity. e^{-i m c} = cos(mc) - i sin(mc) Then I tried to sum over the 2 terms separately...

Hello rude man! We've learned the convention that you usually leave out the dot product sign if it's clear from context how it's meant to be. Just like you'd write 2x instead of "2 times x", we write \vec{A}\vec{B} instead of \vec{A} \cdot \vec{B} :smile: I don't think the + or - signs are...

I have a dipole such as: \rho(\vec{r}) = q \delta(\vec{r} - \vec{a}) - q \delta(\vec{r} + \vec{a}) with \vec{a} = a \vec{e}_x. I have to show that the energy in a constant external field \vec{E} is: V = - 2 q \vec{a} \vec{E} My calculations so far: With the formula...

Thank you. :smile:

So to come back to my initial question, in region 2 it would be Q + \frac{4 \pi \rho_0 (r^3-R_1^3)}{3}? :redface:

But then again why isn't Q included in region 2 as well? In that case I have a Gaussian spherical surface with radius R_1 < r < R_2 in mind. That does include the point charge Q in the center as well? Can you somewhat understand my understanding problem?

Hmm, r > R_2 I guess so it encloses my entire spherical shell? Then Q + \frac{4 \pi \rho_0 (R_2^3-R_1^3)}{3} is correct (total charge inside + total charge in the shell)?

I have a sphere in mind!