Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function - A. X. Martins; R. A. S. Paiva; G. Petronilo; R. R. Luz; R. G. G. Amorim; S. C. Ulhoa; T. M. R. Filho (Advances in High Energy Physics)
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.