Asymptotics of the discrete spectrum for a radial Schrödinger operator with nearly Coulomb potential (Q1179081)

The paper is the continuation of author's previous papers [Theor. Math. Phys. 76, 379 (1988)] devoted to obtain the asymptotic behaviour of the discrete spectrum for the Schrödinger operator with Coulomb potential, of compact support. An asymptotic formula for the discrete spectrum is obtained. It shows that the quantum defect tends to a constant as the principle quantum number tends to infinity. An explicit expression of this constant is obtained. The method is based on the transition from the differential equation to an equivalent integral equation of Volterra type. It starts with a special representation of a singular Whittaker function followed by the derivation of estimates for solutions of the integral equation of Volterra type. Finally, asymptotics of the spectrum are obtained.