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Proceedings of the Estonian Academy of Sciences

A global, dynamical formulation of quantum confined systems; pp. 290–293

Nuno Costa Dias, João Nuno Prata

Published Oct 28, 2010• 1 citation
Publisher

Abstract

A brief review of some recent results on the global self-adjoint formulation of systems with boundaries is presented. We concentrate on the 1-dimensional case and obtain a dynamical formulation of quantum confinement.
DOI
10.3176/proc.2010.4.06

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The Weyl–Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation as well as the dynamical equation do not display the expected solutions. In this paper, we review some previous results on 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.
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