Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions

René Carmona, Wen Chen Masters, Barry Simon

Research output: Contribution to journalArticle

144 Scopus citations

Abstract

Nonrelativistic Schrödinger operators are perturbations of the negative Laplacian and the connection with stochastic processes (and Brownian motion in particular) is well known and usually goes under the name of Feynman and Kac. We present a similar connection between a class of relativistic Schrödinger operators and a class of processes with stationary independent increments. In particular, we investigate the decay of the eigenfunctions of these operators and we show that not only exponential decay but also polynomial decay can occur.

Original languageEnglish (US)
Pages (from-to)117-142
Number of pages26
JournalJournal of Functional Analysis
Volume91
Issue number1
DOIs
StatePublished - Jun 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis

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