Probabilistic representation and fall-off of bound states of relativistic Schrödinger operators with spin 1/2

Fumio Hiroshima, Takashi Ichinose, József Lorinczi

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

A Feynman-Kac type formula for relativistic Schrödinger operators with unbounded vector potential and spin 1=2 is given in terms of a three-component process consisting of a Brownian motion, a Poisson process and a subordinator. This formula is obtained for unbounded magnetic fields and magnetic fields with zeros. From this formula an energy comparison inequality is derived. Spatial decay of bound states is established separately for growing and for decaying potentials by using martingale methods.

Original languageEnglish
Pages (from-to)189-214
Number of pages26
JournalPublications of the Research Institute for Mathematical Sciences
Volume49
Issue number1
DOIs
Publication statusPublished - 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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