Recent content by olgranpappy

For example, non-relativistic quantum electrodynamics--the kind usually taken as the starting point for theoretical developments in condensed matter physics... this contains non-local terms in the hamiltonian wherein creation and annihilation operators at different points in space multiply each...

first work out the commutators: [p,x]=? [p,x^2]=? [p,x^3]=? and so on... Then expand V as a power series and use the above commutators to prove the relation.

I think the question is worded very poorly, but probably they are looking for some statement about the Hamiltonian since they also ask about energy. For example, if the hamiltonian is the sum of single-particle operators (operators only depending on a single coordinate and momentum) then a...

how about using: 2cot(x)=((1/tan(x/2)) - tan(x/2)) then plug in for tan(x/2), where x=a\sqrt(2m(E+V)/hbar^2), using the LHS of your first expression... and I guess be careful about signs and square roots.

yeah sure, that is an operator that connects those states. If they just want an operator in particular then that answer the question. Here's something to think about, though. For example, suppose k=1. Then your operator is a + a^\dagger but how about the operator a + a^\dagger +...

yeah, presumably there are lots of representations which are unitarily equivalent to the standard representation... I'm not sure what you are asking? As far as I know unitary equivalence means a matrix A is related to another matrix B via A=UBU^\dagger where U is unitary. So take any unitary...

no, that is not correct

depends... what's \mathcal{L}_H and what's u?

In the last equality the first two "A"s should be written as "A(t)"s... Because they are e^{iHt}Ae^{-iHt}, since you can pass the e^{iHt} past H.

Yes, and in the same way as for a square lattice. In any lattice you still have basis vectors. For example, in the hexagonal lattice the basis vectors can be chosen to look like they point along two sides of a triangle. Call one of these \vec R_1 and the other \vec R_2. You can pick some N_1...

Can you post your professor's research article on Octupole correlations? This might hlep us to answer the question because "Octupole correlations" could mean different things in different contexts.

Hi, I just tried to work this out, but I chose a different basis labeling... but perhaps this will be useful to you all the same. Also, in the Hamiltonian you wrote down there seems to be no "k" (wave vector) dependence... was this just a typo? I.e., did you mean e^(ik.X) for T(X)...

Because Zee starts off using the path integral formalism rather than canonical formalism, his proof of Wick's Theorem is really straightforward and just involves doing a bunch of gaussian integrals. The theorem can also be proved using the canonical formalism, but it's a lot more disgusting...

For the first part probably you are required to discuss how the masses vibrate differently for each mode. In which mode are the two masses of the unit cell pushing against one another and in which mode are them pushing with one another. Which mode reduces to a uniform translation of the lattice...

Could be. Could you give us some more context? Do you have the citation for the paper? Cheers, Adam