A Free Particle on a Circle with Point Interaction

Abstract

The quantum dynamics of a free particle on a circle with point interaction is described by a U(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing a number of subfamilies and thereby analyze the spectral structure in detail. We find that the spectrum depends on a subset of U(2) parameters rather than the entire U(2) needed for the Hamiltonians, and that in particular there exists a subfamily in U(2) where the spectrum becomes parameter-independent. We also show that, in some specific cases, the WKB semiclassical approximation becomes exact (modulo phases) for the system.

Plain TeX, 14 pages

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• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
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• Four-Parameter Point-Interaction in 1-D Quantum Systems
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