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Nonlinear stationary solutions of the wigner and wigner-poisson equations

Haas, F. and Shukla, P.K. (2008) Nonlinear stationary solutions of the wigner and wigner-poisson equations. Physics of Plasmas, 15 (11). ISSN 1070-664X

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Abstract

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