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HOMOGENEOUS SCHRÖDINGER OPERATORS ON HALF-LINE

By Laurent Bruneau, Jan Dereziński and Vladimir Georgescu

Abstract

ABSTRACT. The differential expression Lm = − ∂ 2 x + (m2 − 1/4)x −2 defines a self-adjoint operator Hm on L 2 (0, ∞) in a natural way when m 2 ≥ 1. We study the dependence of Hm on the parameter m, show that it has a unique holomorphic extension to the half-plane Re m> −1, and analyze spectral and scattering properties of this family of operators. 1

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.158.2257
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