Resonance selection principle and low energy resonances for a radial Schrödinger operator with nearly Coulomb potential
This paper is devoted to the study of resonances for the radial Schrödinger operator with Coulomb potential perturbed by a compactly supported function. The resonances are defined as poles of an analytic continuation of the quadratic form of the resolvent. One of the main results of the paper is the statement that resonances can be described as roots of the Jost function, like in the non-Coulomb case. Using this result the author proves that all resonances split into infinite sequences of series (corresponding to different values of an angular momentum \(\ell)\) and zero cannot be a point of accumulation of resonances when \(\ell\) is fixed. In order to obtain these results the main tool are estimates for the regular and Jost solutions of the perturbed equation which are obtained from Volterra integral equations for these solutions.
radial Schrödinger operator with Coulomb potential
scientific article; zbMATH DE number 566439
scientific article