Homogeneous Schrödinger operators on half-line

Abstract

The differential expression $L_m=-{\partial }_x^2+(m^2-1/4)x^{-2}$ defines a self-adjoint operator H_m on L^2(0;\infty) in a natural way when $m^2\ge 1$. We study the dependence of H_m 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.

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