Ground state decay for Schrödinger operators with confining potentials

2024/07/12 by Baraniewicz, Miłosz
#26A12 #35K05 #47D08 #60J65 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.09267

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.

Related

• Bulk behaviour of ground states for relativistic Schrödinger operators with compactly supported potentials
• A Schrödinger operator with confining potential having quadratic growth
• Stability of ground state eigenvalues of non-local Schrödinger operators with respect to potentials and applications
• Two-sided bounds on the point-wise spatial decay of ground states in the renormalized Nelson model with confining potentials
• Contractivity and ground state domination properties for non-local Schrödinger operators