Schrödinger equation for the one-particle density matrix of thermal systems: an alternative formulation of Bose-Einstein condensation

Abstract

We formulate a linear Schrödinger equation with a temperature-dependent potential for the one-particle density matrix and obtain the condensation temperature of the Bose-Einstein condensate from a bound-state condition for the Schrödinger equation both with and without the confining trap. The results are in very good agreement with those of the full statistical physics treatment. This is an alternative to the Bose-Einstein condensation in the standard ideal Bose-gas treatment.