Tagged Questions

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Laplace's equation with spherical, cylindrical, and planar symmetry [closed]

Find the general solution to Laplace's equation for spherical symmetry (everything can only depend on $r$, the radius), cylindrical symmetry (everything can only depend on $s$, the radius), and ...
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What are the generators of spherical symmetry?

The title says it all. I think this should be a pretty simple question but I just couldn't find the answer. Ok -- I'll give a bit more context to my question. I'm encountering this in the context of ...
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Symmetry in resistor circuits

Given 6 points that are connected with each other with a resistor of resistance $R$, find the resistance between any two points. (Answer: $R/3$) (All the conducting wires have the same ...
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$\left(H^\dagger H\right)^2$ is invariant under $U(1)\times SU(2)$?

Is it true that $\left(H^\dagger H\right)^2$ is invariant under $U\left(1\right) \times SU\left(2\right)$ where $H$ is the Higgs field $(1,2,1/2)$? Does this invariance imply that its hypercharge ...
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Diagonal matrix in k-space

I'm having some trouble with an integration I hope you guys can help me with. I have that: ${{\mathbf{v}}_{i}}\left( \mathbf{k} \right)=\frac{\hbar {{\mathbf{k}}_{i}}}{m}$ and ...
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Schrödinger function: Separable wave function with even potential function of x

I have done the Problem 2.1 in Griffiths' quantum mechanics, and it seems not making sense to me. What if the wave function isn't symmetric at all? Then obviously the proof doesn't work. The ...
I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...