Recent content by Silicon-Based

This isn't technically a homework problem, but I'm trying to check my understanding of the geometric phase by explicitly calculating the Berry connection for a simple 2x2 Hamiltonian that is not a textbook example of a spin-1/2 particle in a three dimensional magnetic field solved via a Bloch...

The standard reference for open quantum systems is The Theory of Open Quantum Systems by Breuer and Petruccione, which seems well-written but it lacks exercises, as do all the other textbooks I googled. Does someone have a recommendation for a textbook on open quantum systems with problems to...

I'm looking for literature recommendations regarding tensor networks. I never came across singular value decomposition or spectral decomposition in my linear algebra classes, so I need to brush up on the relevant mathematical background as well.

I've joined a group which studies cold atoms a little over two months ago. I was asked to write a Markov Chain Monte Carlo script, which I did, and which turned out really promising. I've been programming in Python for almost a year now so this wasn't too difficult to do. Shortly thereafter, the...

I am looking for a book/notes on the topics mentioned in the title that would be accessible to an undergrad. I have a background in grad quantum and statistical mechanics, but most resources I found on those topics assume a familiarity with QFT, string theory, gauge theory, and general...

For the case when ##B=0## I get: $$Z = \sum_{n_i = 0,1} e^{-\beta H(\{n_i\})} = \sum_{n_i = 0,1} e^{-\beta A \sum_i^N n_i} =\prod_i^N \sum_{n_i = 0,1} e^{-\beta A n_i} = [1+e^{-\beta A}]^N$$ For non-zero ##B## to first order the best I can get is: $$Z = \sum_{n_i = 0,1}...

I'm considering a hydrogen atom placed in an infinite potential on one side of the nucleus, i.e. ##V(x) = +\infty## for ##x < 0##. I require the wavefunctions to be odd in order to satisfy the boundary condition at ##x=0##. By parity of the spherical harmonics only states with ##l## odd are...

This should be a trivial question. I am trying to compute the spherical tensor ##T_0^{(0)} = \frac{(U_1 V_{-1} + U_{-1} V_1 - U_0 V_0)}{3}## using the general formula (Sakurai 3.11.27), but what I get is: $$ T_0^{(0)} = \sum_{q_1=-1}^1 \sum_{q_2=-1}^1 \langle 1,1;q_1,q_2|1,1;0,q\rangle...

That's right; I missed a minus sign which normalized everything.

So I've tried factoring out the eigenkets from the superposed kets in my equation, e.g. ##\cos(\alpha/2)|+\rangle + \sin(\alpha/2)|-\rangle##, and found out that most of the terms cancel. I ended up with the expression ##\cos(\alpha)|\text{singlet}\rangle##. Now I'm only unsure how to...

I'm not sure I understand why I need to do this. Don't the rotation operators act only the corresponding spin states in their Hilbert space, in which case I wouldn't need to find the tensor product? This worked for me when trying to show invariance under rotation about z, unless that was purely...

I have tried doing the obvious thing and multiplied the vectors and matrices, but I don't see a way to rearrange my result to resemble the initial state again: ##(\mathcal{D_{1y}(\alpha)} \otimes \mathcal{D_{2y}(\alpha)} )|\text{singlet}\rangle = \frac{1}{\sqrt{2}}\left[ \begin{pmatrix}...

For ##N = 1 = n_x + n_y + n_z## when you apply the completeness relation you get a sum states in coordinate basis for each ##n_i=1##, for a total of three states, each with an inner product between the coordinate and spherical bases (the bra-kets on the very right in the completeness equation)...

Suppose I have a positive spin-##1/2## eigenstate pointing in the ##z##-direction. If I apply a rotation operator by an angle ##\theta## around the ##z##-axis the state should of course not change. However, if I write it out explicitly, I find something different: $$R_z(\theta)|\uparrow\rangle =...

What I'm confused about is how the representations were obtained from the closure relation. I understand everything before it. I don't see how to get rid of the inner products after making use of the closure relation.