The integral transformation method in the spectral problem for the confining potential

An integral transformation method is used to find the energy spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with an infinitely increasing power-law confining potential. The problem is reduced to an approximate solution of an infinite system of linear algebraic equations. Numerical computations are used to determine the $S$-state spectrum of the Schr$\stackrel{..}{o}$dinger equation with a linearly increasing potential.