Recent content by kakaho345

As in title: Plugging in the definition is straight forward, I am too lazy to type, I will just quote the book Fetter 1971: Up to here everything is very straight forward, in particular, since we are working on free electron gas, ##E=\hbar \omega## However, I have no idea how to arrive...

I was in a PhD program in Physics, I dropped out due to mental health issue, now that I am out of the distress, I actually want to get back to research. But I don't want to once again get into mental health problem. So I wonder if I am allowed to post here and update daily as a blog? Or any...

I see, thanks for replying. Your answer is super relevant and helpful. He didn't explicitly stated Hodge theorem, but he did talked about the Harmonic forms previously. For future people interested, it is in his lecture 3 when he talks about representatives of cohomologies. He mentioned the...

Hello, I have been looking at some differential geometry and watching Hirosi's video lecture online: At 1:03:00, I found that they claimed that there is a correspondence between the Hibert space of the symmetric Hamiltonian and the cohomology of the manifold. I am super new to the subject and...