Unitary equivalence and scattering theory for Stark-like Hamiltonians

Matania Ben-Artzi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let H0 = - Δ + V0(x1), H = H 0 + V(x) be self-adjoint in L2(Rn). V 0 depends only on one coordinate and tends monotonically to ∓ ∞ as x1 → ± ∞. Vis a real H 0-compact potential, short range with respect to V0. In particular, the cases V0(x1) = - (sgn x 1)|x1|α, 0<α≤2 and |V(x)|≤C|x|-1 are included (α = 1 being the Stark effect). It is shown that (a) H is spectrally absolutely continuous over the entire real axis apart from a possible discrete sequence of eigenvalues of finite multiplicity and rapidly decaying eigenfunctions (H0 has no eigenvalues) and (b) the wave operators W±(H,H0) exist and are complete.

Original languageEnglish
Pages (from-to)951-964
Number of pages14
JournalJournal of Mathematical Physics
Volume25
Issue number4
DOIs
StatePublished - 1984
Externally publishedYes

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