Möbius structure of the spectral space of Schrödinger operators with point interaction

Izumi Tsutsui, T. Fülöp, Taksu Cheon

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

The Schrödinger 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 ∈ U(2) that characterizes the extension, and that (ii) the space of distinct spectra is given by the orbifold T2/ℤ2 which is a Möbius 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.

Original languageEnglish
Pages (from-to)5687-5697
Number of pages11
JournalJournal of Mathematical Physics
Volume42
Issue number12
DOIs
Publication statusPublished - Dec 2001

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Point Interactions
operators
Operator
Distinct
Self-adjoint Extension
Quotient Space
quotients
Orbifold
interactions
Parametrization
One Dimension
Strip
Parameter Space
strip
Duality
eigenvalues
Eigenvalue
matrices
Family

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Möbius structure of the spectral space of Schrödinger operators with point interaction. / Tsutsui, Izumi; Fülöp, T.; Cheon, Taksu.

In: Journal of Mathematical Physics, Vol. 42, No. 12, 12.2001, p. 5687-5697.

Research output: Contribution to journalArticle

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