Levinson's theorem for Schroedinger operators with point interaction: a topological approach

Abstract

In this note Levinson theorems for Schroedinger operators in R^n with one point interaction at 0 are derived using the concept of winding numbers. These results are based on new expressions for the associated wave operators.

7 pages

References in corpus (2)

• Finite Energy Sum Rules in Potential Scattering
• Topological boundary maps in physics: General theory and applications

Cited by in corpus (16)

• One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
• Scattering theory for lattice operators in dimension $d\ge 3$
• On the structure of the wave operators in one dimensional potential scattering
• The topological meaning of Levinson's theorem, half-bound states included
• On the wave operators for the Friedrichs-Faddeev model
• Levinson's theorem and higher degree traces for Aharonov-Bohm operators
• New expressions for the wave operators of Schroedinger operators in R^3
• The density of surface states as the total time delay
• Levinson's theorem as an index pairing
• Levinson's theorem: an index theorem in scattering theory
• On the wave operators and Levinson's theorem for potential scattering in R^3
• Does Levinson's theorem count complex eigenvalues ?
• Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example
• Scattering operator and wave operators for 2D Schrödinger operators with threshold obstructions
• Explicit formulas for the Schroedinger wave operators in R^2
• New formulae for the Aharonov-Bohm wave operators