Generalized Rayleigh-Schrödinger perturbation theory in matrix form

Thenested summation symbols (NSS) formalism is used as a starting point to formulate a completely general Rayleigh-Schrödinger perturbation theory (RSPT) scheme. In order to make the theoretical framework practical from a computational point of view, the matrix form for the theory is given in every case. As a result, an algorithmic iterative recipe to compute eigenvalue and eigenvector corrections up to any order is described. Degenerate systems are also treated. At the same time the described procedure allows the computation of eigenvalue and eigenvector derivatives with respect to a set of parameters.

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