ABSTRACT
Perturbation theory has been extensively used in atomic physics and quantum chemistry for accurate determination of properties of complicated systems. Extensive studies demonstrate the effectiveness of this method in incorporating the electron correlation for precise descriptions of many-electron systems. The basic philosophy of this theory is to partition the actual system of interest into an unperturbed part whose mathematical solution is known and a perturbation. The physical quantities associated with the perturbed system are then expressed as corrections in terms of unperturbed functions. There exist two major classes of perturbation theory, namely, Rayleigh-Schrödinger (RS) [45, 46] and Brillouin-Wigner (BW) [47, 48, 49, 50], which stem from the basic architecture of composing the perturbation series. While the RS formulation is the most common, owing to its structural simplicity and size extensivity, the latter, on the contrary, involves an unknown state energy term in the perturbation series. In this chapter, we mostly confine our attention to detailed treatment of time-independent perturbation theory. While the majority of the initial developments relied on the non-degenerate unperturbed part, later developments focused on a quasi-degenerate or degenerate perturbation theories in general.
