Radial Schrödinger equation: The spectral problem

Using the integral transformation method involving the investigation of the Laplace tranforms of wave functions, we find the discrete spectra of the radial Schrödinger equation with a confining power-growth potential and with the generalized nuclear Coulomb attracting potential. The problem is reduced to solving a system of linear algebraic equations approximately. We give the results of calculating the discrete spectra of the $S$-states for the Schrödinger equation with a linearly growing confining potential and the nuclear Yukawa potential.