Variational Method for the Quantum Statistics of Interacting Particles

Abstract

A variational method is developed for calculating the thermodynamic potential of quantum‐mechanical many‐body systems with pair‐wise interactions. The method is based on Peierls' theorem and yields an upper bound to the thermodynamic potential density in the limit of an infinite system. Evaluation and minimization of the bound involves solution of a set of coupled nonlinear integral equations for the distribution function of elementary excitations and for functions defining a unitary transformation from bare particles to elementary excitations. Application of the theory to the BCSmodel of superconductivity reproduces the BCS results, and application to a degenerate imperfect Bose gas gives equations which are shown to be equivalent to those of Tolmachev and Wentzel.