Time operators for one parameter semigroups

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.
Original languageEnglish
Pages (from-to)473-486
Number of pages14
JournalRussian Journal of Mathematical Physics
Volume10
Issue number4
Publication statusPublished - Oct 2003

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Fingerprint Dive into the research topics of 'Time operators for one parameter semigroups'. Together they form a unique fingerprint.

  • Cite this