A limiting absorption principle for Schrödinger operators with Von Neumann-Wigner type potentials

Allen Devinatz, Richard Moeckel, Peter Rejto

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper we prove the main step in establishing a limiting absorption principle for von Neumann-Wigner type Schrödinger Hamiltonians of the form -Δ+csinb|x|/|x|+V(x), where V(x) is a short range potential. The first fundamental step is to obtain a limiting absorption principal for the "free" operator -Δ+csinb.|x|/|x|. The free operator is unitarily equivalent to a direct sum of ordinary differential operators. We obtain uniform estimates for the resolvents of these ordinary differential operators. by obtaining uniform estimates for the Weyl-Green kernels of these resolvents. In turn, these latter estimates require uniform estimates on the Wronskians of certain generalized eigen-solutions of these differential operators.

Original languageEnglish (US)
Pages (from-to)13-68
Number of pages56
JournalIntegral Equations and Operator Theory
Volume14
Issue number1
DOIs
StatePublished - Jan 1 1991

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