Estimates for fundamental solutions and spectral bounds for a class of Schrodinger operators

摘要

We study a class of Schrodinger operators of the form L-epsilon := -epsilon(2) d(2)/ds(2) + V, where V : R -> R is a non-negative function singular at 0, that is V(0) = 0. Under suitable assumptions on the potential V, we derive sharp lower and upper bounds for the fundamental solution h(epsilon). Moreover, we obtain information on the spectrum of the self-adjoint operator defined by L-epsilon in L-2 (R). In particular, we give a lower bound for the eigenvalues. (c) 2007 Elsevier Inc. All rights reserved.