Spectral and scattering theory for the adiabatic oscillator and related potentials

Matania Ben-Artzi*, Allen Devinatz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We consider the Schrödinger operator H = -Δ+V(r) on R n, where V(r) = a sin(br α)/r β+VS(r), VS(r) being a short range potential and α>0, β>0. Under suitable restrictions on α, β, but always including α = β = 1, we show that the absolutely continuous spectrum of H is the essential spectrum of H, which is [0, ∞), and the absolutely continuous part of H is unitarily equivalent to -Δ. We use these results to show the existence and completeness of the Møller wave operators. Our results are obtained by establishing the asymptotic behavior of solutions of the equation Hu = zu for complex values of z.

Original languageEnglish
Pages (from-to)594-607
Number of pages14
JournalJournal of Mathematical Physics
Volume20
Issue number4
DOIs
StatePublished - 1978
Externally publishedYes

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