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
Original language | English |
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Journal | Physics of Plasmas |
Volume | 15 |
Issue number | 11 |
DOIs | |
Publication status | Published - Nov 2008 |
Keywords
- Clebsch-Gordan coefficients
- plasma instability
- Poisson equation