Determination of discrete spectrum of radial Schr$\stackrel{..}{o}$dinger equation with arbitrary attracting potential

The method of integral transforms related to the study of the Laplace images of wave functions is applied to find the discrete spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with short- and long-range attracting potentials of general form. The summation of the series has been performed in matrix elements of the characteristic equation, which are represented as formal expansions in inverse powers of the energy. The possibilities of the method have been demonstrated on the example of the $S$-state of the Schr$\stackrel{..}{o}$dinger equation with the Huelten potential. The suggested method can also be successfully used for other potentials.