-δ plus a bad potential

H. P. McKean

Research output: Contribution to journalArticle

Abstract

The purpose of this paper is to associate with -Δ+V(x) a self-adjoint operator in case V is nonnegative. This has been done in many ways by previous authors under a variety of conditions. The point of the present work is to do this under conditions applying to, e.g., any many-body potential, the only requirements being that V:R 3n→[0,∞] be continuous and that V-1(∞) be not too large in the sense of volume and/or capacity; especially, no conditions of growth are imposed upon V. The method of proof is probabilistic, being based upon familiar properties of the Brownian motion.

Original languageEnglish (US)
Pages (from-to)1277-1279
Number of pages3
JournalJournal of Mathematical Physics
Volume18
Issue number6
StatePublished - 1976

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Brownian movement
Self-adjoint Operator
Brownian motion
Non-negative
operators
requirements
Requirements

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

McKean, H. P. (1976). -δ plus a bad potential. Journal of Mathematical Physics, 18(6), 1277-1279.

-δ plus a bad potential. / McKean, H. P.

In: Journal of Mathematical Physics, Vol. 18, No. 6, 1976, p. 1277-1279.

Research output: Contribution to journalArticle

McKean, HP 1976, '-δ plus a bad potential', Journal of Mathematical Physics, vol. 18, no. 6, pp. 1277-1279.
McKean, H. P. / -δ plus a bad potential. In: Journal of Mathematical Physics. 1976 ; Vol. 18, No. 6. pp. 1277-1279.
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