The Dalgarno-Lewis Technique

Abstract

In treating quantum mechanical systems which do not admit to exact solutions for their energy levels and corresponding wavefunctions one has at one’s disposal as mentioned in a previous chapter the variational approach (Chapter 10). This however, is restricted to the ground and possibly first excited state (if the Hamiltonian commutes with the parity operator). For other states (and even for the ground state if one requires greater accuracy or additional information against which to juxtapose the variational results) one must fall back on the straightforward application of perturbation theory (Chapter 11) which is generally tedious and at best only approximate. This is because, for other than the first-order results, using perturbation theory one has to evaluate infinite sums in each order (cf. expressions (11.14), (11.15) which one generally approximates by selecting only a few terms which arise to that order.