Stationary scattering theory for repulsive Hamiltonians
Kyohei Itakura
TL;DR
This paper develops a stationary scattering theory framework for repulsive Hamiltonians, establishing key properties like wave operators, scattering matrix unitarity, and eigenfunction asymptotics using radiation condition bounds.
Contribution
It introduces a comprehensive stationary scattering theory for repulsive Hamiltonians, including existence, completeness, and characterization of eigenfunctions.
Findings
Existence and completeness of stationary wave operators
Unitarity of the scattering matrix
Characterization of eigenfunction asymptotics
Abstract
In the present paper we discuss stationary scattering theory for repulsive Hamiltonians. We show the existence and completeness of stationary wave operators and unitarity of the scattering matrix. Moreover we completely characterize asymptotic behaviors of generalized eigenfunctions with minimal growth in terms of the scattering matrix. In our argument the radiation condition bounds for limiting resolvents play major roles. In fact, it is used to construct the stationary wave operators.
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