Ground state decay for Schrödinger operators with
confining potentials
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.