a1 PMMS/CNRS, 3A Avenue de la Recherche Scientifique, 45071 Orleans Cedex 2, France
The expansion of a quantum electron gas (non-relativistic, no spin) is investigated via the one-particle Schrödinger–Poisson model. Classically, the nonlinear term enhances the formation of a very regular asymptotic state. By means of rescaling methods, we conjecture that the quantum asymptotic solution is identical to the classical one. Subsequent numerical simulations confirm the above conjecture and define precisely the way in which the classical limit is approached.
(Received April 13 1993)
(Revised July 28 1993)