Well, it's a homework problem in the sense that I happen to be working on it at my home, but, no, I'm not in school anymore. In Quantum Mechanics we use determinants to enforce the Pauli principle, which says that anytime two electrons are exchanged the wave function has to change sign. In most Quantum Mechanical packages (for example, PyQuante, http://pyquante.sf.net, which I wrote some years ago, is a Python based quantum chemistry package) we don't actually have to evaluate a determinant, we just evaluate the effect of the two-electron operators on the permuted wave function. However, I'm working on some quantum monte carlo codes where I'm trying to keep track of configuration spin functions, which requires me to count every time I flip orbitals.
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