  This paper is concerned with the study of one-body dissipation effects in
idealized models resembling a nucleus. In particular, we study the quantum
mechanics of a free particle that collides elastically with the slowly moving
walls of a Bunimovich stadium billiard. Our results are twofold. First, we
develop a method to solve in a simple way the quantum mechanical evolution of
planar billiards with moving walls. The formalism is based on the {\it scaling
method} \cite{ver} which enables the resolution of the problem in terms of
quantities defined over the boundary of the billiard. The second result is
related to the quantum aspects of dissipation in systems with complex spectra.
We conclude that in a slowly varying evolution the energy is transferred from
the boundary to the particle through Landau$-$Zener transitions.
