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Computational Science

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  • $\begingroup$ I lost you at the third equation. Why do you need to solve a generalized eigenvalue problem to compute the eigenvectors and eigenvalues of a Hermitian matrix? What's wrong with a normal eigensolver? Where did that S pop out of? $\endgroup$ Commented Jun 15, 2018 at 14:01
  • $\begingroup$ The reason why a generalized EVP has to be solved is intrinsic to this problem, I should have said that. It has a physical background: basically, the Schrödinger eqn. is solved for the case that the ansatz wave function is represented via a non-orthogonal basis set $\{\phi_i\}$. This yields the overlap matrix $S_{ij}=\langle\psi_i|\psi_j\rangle$. $\endgroup$ Commented Jun 15, 2018 at 14:28
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    $\begingroup$ So what is the function that you really have to compute? It's not the one in the first equation, is it? Where does $S$ appear in it? $\endgroup$ Commented Jun 15, 2018 at 14:29