Nonlinear stationary solutions of the wigner and wigner-poisson equations

F. Haas, P.K. Shukla

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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 languageEnglish
JournalPhysics of Plasmas
Issue number11
Publication statusPublished - Nov 2008


  • Clebsch-Gordan coefficients
  • plasma instability
  • Poisson equation

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