The inverse decay problem

L. P. Horwitz, J. A. LaVita, J. P. Marchand

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


Let Uscript K(t) be a one-parameter operator family of positive type in a Hilbert space script K and U(t) its minimal unitary dilation with infinitesimal generator H. If Uscript K(t) is a contractive semigroup, then H is not positive. If in addition Uscript K(t)→0 for t→∞, then there exists a state φ ∈ script K on which H is not defined. We interpret these and other results in the context of the quantum-mechanical theory of unstable particles and the scattering theory of Lax and Phillips.

Original languageEnglish
Pages (from-to)2537-2543
Number of pages7
JournalJournal of Mathematical Physics
Issue number12
StatePublished - 1971
Externally publishedYes


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