Scattering theory for the Klein-Gordon equation
Abstract
A study of the scattering theory for the Klein-Gordon equation is presented. A criterion for the self-adjointness and the invariance of the essential spectrum of the perturbed operator is given. The Lippman-Schwinger equation for the generalized eigenfunctions is examined utilizing an approximation of the potentials by bounded potentials with compact support. Generalized Fourier transforms are determined which yield the unitary equivalence of the free operator and the absolutely continuous part of the perturbed operator. Provided that they exist, the completeness of the wave operators is demonstrated.
- Publication:
-
Functiones et Approximatio Commentarii Mathematici
- Pub Date:
- 1980
- Bibcode:
- 1980FACM....8...13E
- Keywords:
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- Klein-Gordon Equation;
- Wave Scattering;
- Eigenvalues;
- Fourier Transformation;
- Operators (Mathematics);
- Potential Theory;
- Physics (General)