相空间中吸引性非线性Schrdinger方程与Bose-Einstein凝聚

Attractive nonlinear Schrdinger equation and Bose-Einstein condensate in phase space

在Torres-Vega和Frederick量子相空间表象框架下,获得了用于模拟Bose-Einstein凝聚态的吸引性非线性Schrdinger方程的严格解.所得到的本征函数可通过"类Fourier"投影变换分别投影到位移空间和动量空间中去,从而得到相应空间中的本征函数.作为例子,探讨了一类带有双曲函数的本征解的性质.

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of attractive nonlinear Schrǒdinger equation are solved, which models the Bose-Einstein condensate. The eigenfunctions in position and momentum spaces can be obtained through the “Fourier-like” projection transformation from the phase-space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.