Study of discrete spectrum of radial Schr$\stackrel{..}{o}$dinger equation with nuclear Coulomb potential

The method of integral transformations related to studying the Laplace images of wave functions is applied to determine the discrete spectrum of radial Schr$\stackrel{..}{o}$dinger's equation with arbitrary attraction potential. The summation of series has been performed in matrix elements of the characteristic equation, which are represented in the form of formal expansions in inverse powers of energy. The possibilities of the method have been demonstrated with the examples of the generalized Yukawa potential and the screened Coulomb potential; the method can also be successfully applied to other potentials.