Homogeneous Schrödinger Operators on Half-Line

Abstract

The differential expression Lm=-∂x2+(m2-1/4)x-2 defines a self-adjoint operator Hm on L2(0, ∞) in a natural way when m2 ≥ 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. © 2011 Springer Basel AG.