Abstract
Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of repulsive nonlinear Schrödinger equation are solved, which models the dilute-gas Bose-Einstein condensate. The eigenfunctions in position and momentum spaces can be obtained through the “Fourier-like” projection transformation from the phase-space eigenfunctions. It shows that the wave-mechanics method in the phase-space representation could be extended to the nonlinear Schrödinger equations. The research provides the foundation for the approximate calculation in future.
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