New formulae for the wave operators for a rank one interaction
Serge Richard, Rafael Tiedra de Aldecoa
TL;DR
This paper introduces new mathematical formulae for wave operators in a quantum scattering model with a rank one interaction, and establishes a topological version of Levinson's theorem for this system.
Contribution
It provides novel formulae for wave operators and a topological Levinson's theorem in a rank one perturbation model.
Findings
New formulae for wave operators derived
Topological Levinson's theorem established
Enhanced understanding of rank one scattering systems
Abstract
We prove new formulae for the wave operators for a Friedrichs scattering system with a rank one perturbation, and we derive a topological version of Levinson's theorem for this model.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Mathematical Analysis and Transform Methods