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The one-dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem. (English) Zbl 0738.35077
The Wigner-Poisson equation governs the evolution of the Wigner function, a quantum mechanical quasidistribution function of electrons on the space-velocity phase space under the action of a selfconsistent Coulomb potential. The existence of a solution of the Wigner-Poisson problem is shown by expanding the solution into a series of solutions of the Schrödinger equation, and the convergence of the solutions of the Wigner-Poisson problem to a generalized solution of the Vlasov-Poisson problem in the classical limit are shown.
Reviewer: H.Steinrück

35Q40 PDEs in connection with quantum mechanics
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
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