Attractive Nonlinear Schrödinger Equation and Bose-Einstein Condensate in Phase Space

Abstract

In this paper, we solve the rigorous solutions of attractive nonlinear Schrödinger equation which models the Bose-Einstein condensate, within the framework of the quantum phase space representation established by Torres-Vega and Frederick. By means of the “Fourier-like” projection transformation, we obtain the eigenfunctions in position and momentum spaces from the phase space eigenfunctions. As an example, we discuss the eigenfunction with a hypersecant part.