Letters in Mathematical Physics

, Volume 45, Issue 1, pp 33-47

First online:

Symmetries of Schrödinger Operator with Point Interactions

  • S. AlbeverioAffiliated withInstitute of Mathematics, Ruhr-Universität
  • , L. DabrowskiAffiliated withSISSA
  • , P. KurasovAffiliated withAlexander von Humboldt fellow, Institute of Mathematics, Ruhr-Universität, Bochum Department of Mathematics, Stockholm University; Department of Mathematical and Computational Physics, St. Petersburg University

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The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon.

Schrödinger operators symmetries extension theory point interactions exactly solvable models.