On the derivation of generalized master equations

Abstract

It is pointed out that the derivation of the Van Hove-Janner-Swenson master equations for the probability and interference functions describing the time evolution of a quantum mechanical system requires no more than a trivial identity involving the diagonal part of the resolvent operator, together with a straightforward definition for casting the equations into gain-loss form. We thus have a very simple derivation of these equations. We also present an alternative, less direct, derivation, which we use to elucidate the relationship between the Van Hove-Swenson formalism and that of Zwanzig; a brief outline of the latter is also given.