English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We discuss the quantum Lax-Phillips theory of scattering and unstablesystems. In this framework, the decay of an unstable system is described by asemigroup. The spectrum of the generator of the semigroup corresponds to thesingularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex)spectrum of the generator of the semigroup, associated with resonances, thedecay law is exactly exponential. The states corresponding to these resonances(eigenfunctions of the generator of the semigroup) lie in the Lax-PhillipsHilbert space, and therefore all physical properties of the resonant states canbe computed.  We show that the Lax-Phillips $S$-matrix is unitarily related to the$S$-matrix of standard scattering theory by a unitary transformationparametrized by the spectral variable $\sigma$ of the Lax-Phillips theory.Analytic continuation in $\sigma$ has some of the properties of a methoddeveloped some time ago for application to dilation analytic potentials.  We work out an illustrative example using a Lee-Friedrichs model for theunderlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Representation of quantum mechanical resonances in the Lax–Phillips Hilbert space