Numerical calculation of the discrete spectra of one‐dimensional Schrödinger operators with point interactions

Abstract

In this paper, we consider one‐dimensional Schrödinger operators Sq on with a bounded potential q supported on the segment and a singular potential supported at the ends h0, h1. We consider an extension of the operator Sq in defined by the Schrödinger operator and matrix point conditions at the ends h0, h1. By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator . Moreover, we provide closed‐form expressions for the eigenfunctions and associate functions in the Jordan chain given in the form of power series of the spectral parameter. The validity of our approach is proven in several numerical examples including self‐adjoint and nonself‐adjoint problems involving general point interactions described in terms of δ‐ and δ′‐distributions.