THE 3-DIMENSIONAL WIGNER-POISSON PROBLEM - EXISTENCE, UNIQUENESS AND APPROXIMATION

We prove the existence of a unique, global classical solution of the quantum Vlasov-Poisson problem posed on the phase space R(x)3 x R(v)3. The proof is based on a reformulation of the quantum Vlasov-Poisson problem as a system of countably many Schrodinger equations coupled to a Poisson equation for the potential. The Schrodinger-Poisson problem is first analysed on a bounded domain in R(x)3 and the solution of the whole-space problem is then obtained by a limiting procedure in which the domains 'tend' to R(x)3.