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

TL;DR

This paper introduces a novel Schrödinger equation approach with a temperature-dependent potential to determine the Bose-Einstein condensation temperature, providing results consistent with traditional statistical physics methods.

Contribution

It presents an alternative formulation of Bose-Einstein condensation using a linear Schrödinger equation for the density matrix, differing from standard ideal Bose gas models.

Findings

Results agree well with full statistical physics calculations.

Provides a new method to analyze Bose-Einstein condensation.

Applicable with and without confining traps.

Abstract

We formulate a linear Schrodinger equation with the 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 Schrodinger 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.