Recent content by roya

thank you

I have very little knowledge in general relativity, though I do have a decent understanding of the theory of special relativity. In special relativity, points in space-time can be represented in Minkowski space (or a hyperbolic space) so that the metric tensor (that is derived in order to...

maybe instead of proof, perhaps some suggestions on how to approach the matter in general. basically any direction or anything that could help build some intuition will be very much appreciated...

proof that the "n" brillouin zones are of equal areas? i'm trying to find a way to prove that the brillouin zones are indeed of equal areas. if i draw, for examle, the first 3 or 4 brillouin zones of a cubic 2-dimensional lattice, then it is relatively easy to show geometrically how the parts...

thanks for the response, i think i partially understand my confusion now.had another question, but just figured it out, so thanks again.

what i mean to ask is how does the new wave function look like. the harmonic oscillator for example, H=p^{2}/2m+m\omega^{2}x^{2}/2 if H(x) --> H(x+a) , then the eigenstates represented in the position basis must go through some sort of transformation as well. how do i represent that transformation?

for example, if the hamiltonian of a system is transformed this way: H(x) --> H(x+a) i understand that the tranformation can be represented by a unitary operator U=exp(iap/\hbar) UH(x)U^{*}=H(x+a) but what happens to the wave function? how is it transformed?

oh very nice, this makes it a bit clearer, though i still have one more question. i have covered the missing steps (finding the H acting on the position basis) though one step isn't clear to me. from what i know, the inner product of the two position basis vectors is: <x|x'> = DiracDelta(x-x')...

i can't seem to understand something very basic about the stationary equation (a "simple" eigenvalue problem): H|Y>=E|Y> H - hamiltonian operator Y - an eigenstate or an eigenfunction of the hamiltonian E - the eigenvalue of the eigenstate as far as i understand, the hamilotian...

so a plane in between the two halves will experience pressure due to the force of repulsion, that makes sense, but i can't figure out how to calculate the pressure without finding the electric field (or force for that matter) if you meant something else then i probably just didn't get it

i am not completely sure how that helps... maybe if you could be more specific?

the fact that it is insulated and not conducting makes it possible for the charge to be uniformly distributed throughout the entire sphere. if it was not insulated then charges would not have been bounded and there would have been no electric field inside. the question is originally stated in a...

insulated sphere with a uniform charge density p, correct. thanks for your help, i hope someone else has an idea though.

electromagnetism if the sphere was a conductor then i would have used the pressure sensed by each half a sphere in order to calculate the force (as you suggested), but since the sphere is insulated i can't seem to come up with an idea on how to solve this ...

why would the charge be distributed at the surface if the sphere is insulated?