Resonances in the rigged Hilbert space and Lax-Phillips scattering theory

Y. Strauss

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

The rigged Hilbert space formalism of quantum mechanics provides a framework in which one can identify resonance states and obtain the typical exponential decay law. However, there remain questions of the interpretation and extraction of physical information through the calculation of expectation values of observables. The Lax-Phillips scattering theory provides a mathematical construction in which resonances are assigned with states in a Hilbert space, thus no such difficulties arise. The original Lax-Phillips structure is inapplicable within standard nonrelativistic quantum theory. Through the powerful theory of Hp spaces certain relations between the two theories are uncovered, which suggest that a search for a "unifying" framework might prove useful.

Original languageEnglish
Pages (from-to)2285-2315
Number of pages31
JournalInternational Journal of Theoretical Physics
Volume42
Issue number10
DOIs
StatePublished - 1 Oct 2003
Externally publishedYes

Keywords

  • H spaces
  • Lax-Phillips theory
  • Resonance
  • Rigged Hilbert space
  • Semigroup evolution

ASJC Scopus subject areas

  • Mathematics (all)
  • Physics and Astronomy (miscellaneous)

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