Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function

الملخص EN

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.