Rigorous solutions of a particle in δ potential fields in phase space

Abstract

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of the Schrödinger equations of a particle in the δ potential fields are solved, and the Heisenberg uncertainty principle is interpreted in the phase space. Then it is found that, for the bound state of a particle in the δ potential well, the Wigner distribution function is the special result of the quantum phase-space probability density function with parameter k approaching infinity.