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Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction

Izumi Tsutsui·Tamas Fulop·Taksu Cheon
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Abstract

The Schroedinger operator with point interaction in one dimension has a U(2) family of self-adjoint extensions. We study the spectrum of the operator and show that (i) the spectrum is uniquely determined by the eigenvalues of the matrix U belonging to U(2) that characterizes the extension, and that (ii) the space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius strip with boundary. We employ a parametrization of U(2) that admits a direct physical interpretation and furnishes a coherent framework to realize the spectral duality and anholonomy recently found. This allows us to find that (iii) physically distinct point interactions form a three-parameter quotient space of the U(2) family.

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Izumi Tsutsui, Tamas Fulop, Taksu Cheon. 2001-05-15. Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction. https://doi.org/10.1063/1.1415432

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