  The Weyl-Wigner formulation of quantum confined systems poses several
interesting problems. The energy stargenvalue equation, as well as the
dynamical equation does not display the expected solutions. In this paper we
review some previous results in the subject and add some new contributions. We
reformulate the confined energy eigenvalue equation by adding to the
Hamiltonian a new (distributional) boundary potential. The new Hamiltonian is
proved to be globally defined and self-adjoint. Moreover, it yields the correct
Weyl-Wigner formulation of the confined system.
