Schrodinger equation for the one particle density matrix of thermal   systems: An alternative formulation of Bose-Einstein condensation
  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. 
Subodha Mishra and Peter Pfeifer