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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 44, Fasc. 2,
pages 267 - 277
DOI: 10.37190/0208-4147.00196
Published online 14.3.2025
 

Ground state decay for Schrödinger operators with confining potentials

Miłosz Baraniewicz

Abstract:

We give two-sided estimates of a ground state for Schrödinger operators with confining potentials. We propose a semigroup approach, based on resolvent and the Feynman-Kac formula, which leads to a new, rather short and direct proof. Our results take the sharpest form for slowly varying, radial and increasing potentials.

2010 AMS Mathematics Subject Classification: Primary 47D08; Secondary 60J65, 35K05, 26A12.

Keywords and phrases: eigenfunction, slowly varying potentials, Feynman--Kac formula, heat kernel, integral kernel, resolvent.

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