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Approximations of a General Class of Quantum-Mechanical One-Dimensional Point Interactions by Local Self-Adjoint Interactions

Takaomi Shigehara, H. Mizoguchi, T. Mishima, T. Cheon

Published Dec 31, 1999• 0 citations
Publisher

Abstract

Approximations of a General Class of Quantum-Mechanical One-Dimensional Point Interactions by Local Self-Adjoint Interactions was published in Proceedings of the Ninth International Colloquium on Differential Equations on page 393.
DOI
10.1515/9783112318973-059

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It has always been believed that no self-adjoint and canonical time of arrival operator can be constructed within the confines of standard quantum mechanics. In this Letter we demonstrate the otherwise. We do so by pointing out that there is no a priori reason in demanding that canonical pairs form a system of imprimitivities. We then proceed to show that a class of self-adjoint and canonical time of arrival (TOA) operators can be constructed for a spatially confined free particle. And then discuss the relatiobship between the non-self-adjointess of the TOA operator for the unconfined particle and the self-adjointness of the confined one.