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

In this paper, we consider one-dimensional Schrödinger operators S_q on (Formula presented.) with a bounded potential q supported on the segment [h₀, h₁] and a singular potential supported at the ends h₀, h₁. We consider an extension of the operator S_q in (Formula presented.) defined by the Schrödinger operator (Formula presented.) 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 Hq. 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.