Recent content by physicsxanime

Thanks so much! If you have spare time, I would really benefit from knowing your motivation on how you come up with a solution and that how one can anticipate the result before the calculation. For now, it seemed to me that you either know the existence of such group or you don't. At the end of...

Yes, of course. I am just stupid. Let's shift the energy scale so that the atomic energy at 1s is 0. Then the Hamiltonian is $$ \begin{pmatrix} 0 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 0 \end{pmatrix} $$ The eigenenergies and corresponding eigenvectors are ##\lambda_1 = -1##, ##\lambda_2 = -1##...

It is from entrance exam at UBC. https://phas.ubc.ca/graduate-program-comprehensive-exam-guidelines-phd-students In particular it is from 2010. https://phas.ubc.ca/sites/default/files/shared/comp2010.pdf

Yes, I should be more careful. The proof is comparing second condition from question with the hermitian conjugate of it, we have: $$AA = A^\dagger A^\dagger$$ This can be satisfied only with either ##AA=A^\dagger A^\dagger=0## or ##A^\dagger = \pm A## Then I compare and by imposing imposing...

A. I can show that A is either hermitian or antihermitian by $$(B^\dagger B=1-A^2)^\dagger$$ $$B^\dagger B=1-A^\dagger A^\dagger$$ comparing, we know that $$A^\dagger = \pm A$$ I don't know how I can make use of the communtation relation to get hermiticity of B. But I know that A and B must have...

I am preparing for graduate prelim exam: My attempt is that, I have three sites for each of the electron to be at, each of them are 1s orbital. Also, electron has a spin 1/2. So, I think the Hilbert space would be quite large, I have state of both electron on each site 1, 2, 3 with singlet...

I have a standard undergrad background + some grad experience. (I switched from cosmology when I get my master to CMT). Basically, I am fine with quantum mechanics, I took QFT before but quite rusty. As for math, I am fine with complex analysis, differential equations, no good on group theory...

For context: I will work on more or less green's function calculations of strongly coupled electrons/phonons systems in the future

TL;DR Summary: I am asking for how to study CMT Any advice in connecting concepts and building intuition for condensed matter? Sometimes I can do some problems operationally, but I can't see connection between different problems and doesn't have a mental model or intuition? I can think of read...

I can solve it using recurrence relation: https://app.conceptboard.com/board/n11a-y61a-o584-90z4-rofy Not sure how to proceed with Lehmann representation, maybe it is not possible I don't know.

I also love suskind's QM book: https://www.amazon.ca/Quantum-Mechanics-Theoretical-Leonard-Susskind/dp/0465062903 Personally I don't like to start QM from talking about wave function and solving differential equation, I got lost easily without understanding the essence of QM. This book started...

Good point! I think advice from people who knows the stuff is very valuable indeed! However, there are a few advantage to have study group. 1. We engage in a more active learning. Each of the study mate are not expert, so we need to all work super hard to clear some concepts. 2. It is also much...

Hi Pholks, I just change my field of study from cosmology to condensed matter and I have a severe lack of knowledge in condensed matter. Having only some concepts in quantum mechanics and field theory, I would like to ask if there are anyone who wants to setup a weekly study group to discuss...

Honestly, I have no real idea. I know for sure the equation connects the initial state ##|\Psi^N_0>##to a final state ##|\Psi^{N+1}_0>##, ##E## is the energy and ##E^N_0## etc are the energy of the initial state and final state. I also know that these energy are related to conduction band and...

Hi pholks, I am starting my career as a grad student in condensed matter physics. Wish me luck. Also wish everyone attain your dreams!