Asymptotic analysis of the quantum Liouville equation

Abstract

We present an asymptotic analysis of the quantum Liouville equation with respect to the Planck's constant, which models the temporal evolution of the (quasi)distribution of an ensemble of electrons under the action of a potential. We consider two cases: firstly a smooth potential, and secondly a potential modelled by a δ‐distribution. In both cases the zeroth‐order term behaves classically. In the smooth case the classical Liouville equation is satisfied and in the case for the δ‐potential an interface condition is derived, so that everything is reflected at the potential barrier. Copyright © 1990 John Wiley & Sons, Ltd