Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

Details Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

2008-07-24

arxiv.org/abs/0807.3941v2

Physics

Quantum Physics

7 figures

Scientific paper

10.1063/1.3008047

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed.

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