Abstract: The Wigner functions play a significant role in quantum mechanics, quantum optics, thermodynam- ics and quantum statistics. Therefore, it has high research value to investigate the Wigner functions for neutral par- ticles with structure that moving in an external electromagnetic field. In this paper, first, we introduce the proper- ties and application of Wigner function. Then, we provide the Hamihonian of the polarized atom using the symmet- ric gauge. At last, by using Bopp shift, we solve the energy eigenvalue equation With the Moyal-Weyl star product, and obtain the energy levels and Wigner functions of the neutral particles in an external electromagnetic field.

Key words: Wigner functions, neutral particles, Moyal-Weyl star product