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1. ### Calculation of the Berry connection for a 2x2 Hamiltonian

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...
2. ### Quantum Open Quantum Systems textbooks with exercises?

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...
3. ### Quantum Tensor networks and tensor algebra

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...
5. ### High Energy Introductory notes on AdS/CFT or black hole thermodynamics

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...

9. ### Invariance of a spin singlet under rotation

That's right; I missed a minus sign which normalized everything.
10. ### Invariance of a spin singlet under rotation

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...
11. ### Invariance of a spin singlet under rotation

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...
12. ### Invariance of a spin singlet under rotation

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}...
13. ### Sakurai 3.21, Cartesian eigenbasis representation

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)...

43. ### Block on a wedge (calculus)

Homework Statement A block of mass m is placed on a rough wedge inclined at an angle α to the horizontal, a distance d up the slope from the bottom of the wedge. The coefficient of kinetic friction between the block and wedge is given by µ_0x/d, where x is the distance down the slope from the...
44. ### Invariant mass problem, elastic collision

E02 doesn't cancel due to the factor of two in the equation of energy conservation. Getting sine out of cosine messes things up as well.
45. ### Invariant mass problem, elastic collision

I end up with $$c^2p^2=\frac{(3E_0+mc^2)(E_0-mc^2)}{12-16\sin^2(\alpha)}$$
46. ### Invariant mass problem, elastic collision

I get results like mc2(E0-mc2)=2γm2cos2(α)c2, where γ is of the protons after the collision. But again, I should be able to solve the question without introducing any gammas, but I don't see a way to apply conservation of momentum without doing so.
47. ### Invariant mass problem, elastic collision

E0 is the total energy of the proton in motion, E0+mc2 is the total energy of the system, which is equally distributed between both protons after the collision.
48. ### Invariant mass problem, elastic collision

When I use conservation of energy (Ef=(E0+mc2)/2) the algebra seems to lead nowhere. Also, presumably, I should ideally not introduce any gammas.
49. ### Invariant mass problem, elastic collision

b). I would refrain from using conservation of momentum since that is specifically mentioned in part c (which I didn't include in the picture), and here it asks to equate the invariant masses.
50. ### Invariant mass problem, elastic collision

fHomework Statement Question b: Homework Equations E2=c2p2+m2c4 The Attempt at a Solution We have c2pinitial2=E02-m2c4, and Ef2=c2p2+m2c4 for each outgoing proton. Combining those equations we get c2p2=Ef2-E02+c2pinitial2. I don't know where to go from here.