A model in perturbation theory

Abstract

We consider a model in the perturbation theory where the Hamiltonian H is a sum of a multiplication operator H 0 by |x| 2 l in the space L 2(ℝd) and of an integral operator V with oscillating kernel. We find conditions for the coincidence of the essential spectra of the operators H 0 and H and for the existence and completeness of the wave operators relating H 0 and H.KeywordsPerturbation TheoryIntegral OperatorOperator VersusEssential SpectrumWave OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.