A modified Lax-Phillips scattering theory for quantum mechanics

Y. Strauss

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.

Original languageEnglish
Article number073501
JournalJournal of Mathematical Physics
Volume56
Issue number7
DOIs
StatePublished - 1 Jul 2015

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint

Dive into the research topics of 'A modified Lax-Phillips scattering theory for quantum mechanics'. Together they form a unique fingerprint.

Cite this