Spectral problem for the Schr$\stackrel{..}{o}$dinger radial equation

A method for determining the spectrum of the Schrodinger radial equation with some retaining and attractive potentials has been suggested. The method is related to a study of Laplace images of wave functions. The problem reduces to solving an infinite system of linear algebraic equations. Power potentials and their combinations with the Coulomb potential and the Yukawa potential have been studied extensively.