The Wigner–Poisson-[formula omitted] system in Wiener algebra.

In this paper, we concern over a class of the Wigner–Poisson- X α system introduced and developed by Bao et al. (2003), Mauser (2001) and Stimming (2005), respectively. The model describes the quantum mechanical motion of particles under the influence of the nonlocal Hartree potential and a local power term (exchange potential). The existence and uniqueness of local mild solution to the n -dimensional ( n = 1 , 3 ) Cauchy problems are established on the space of some integrable functions whose inverse Fourier transforms are also integrable. [ABSTRACT FROM AUTHOR]