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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...
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...
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,...
