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

Tsutsui, Izumi; Fulop, Tamas; Cheon, Taksu

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

Authors

Tsutsui, Izumi

Fulop, Tamas

Cheon, Taksu

Description

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.
16 pages, 2 figures