文章基本信息

标题：Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function
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作者：A. X. Martins ; R. A. S. Paiva ; G. Petronilo 等
期刊名称：Advances in High Energy Physics
印刷版ISSN：1687-7357
电子版ISSN：1687-7365
出版年度：2020
卷号：2020
页码：1-6
DOI：10.1155/2020/7010957
出版社：Hindawi Publishing Corporation
摘要：In this work, we study symplectic unitary representations for the Galilei group. As a consequence a nonlinear Schrödinger equation is derived in phase space. The formalism is based on the noncommutative structure of the star product, and using the group theory approach as a guide a physically consistent theory is constructed in phase space. The state is described by a quasi-probability amplitude that is in association with the Wigner function. With these results, we solve the Gross-Pitaevskii equation in phase space and obtained the Wigner function for the system considered.