2:34 AM
2

On page. 139 of Carroll's GR book, during the discussion of Killing vectors, he quotes an explicit coordinate basis representation for the Killing vectors on $S^2$: \begin{array}{l} R=\partial_{\phi} \\ S=\cos \phi\,\partial_{\theta}-\cot \theta \sin \phi\,\partial_{\phi} \\ T=-\sin \phi\,\partia...

16 hours later…
6:18 PM
2

The second law of thermodynamics states that the entropy in an isolated system cannot decrease This seems intuitive when considering a low entropy system transitioning to a higher entropy state, but very counterintuitive when considering a system that is currently at the greatest possible entro...

2 hours later…
8:22 PM
4

In studying the Hartree-Fock method for solving systems of interacting particles, I have often found that the method is referred to as a mean-field approach. Wikipedia's page for instance says that the mean-field approximation is implied. I don't see why this is the case though. In the HF method,...