Asymptote of retaining potentials and spectrum of the radial Schr$\stackrel{..}{o}$dinger equation. Quasiclassical approximation

By means of a method based on the use of the quasiclassical quantization condition, the asymptotic formulas, $(r \to \infty)$ for the correction $\Delta V(r)$ to the reference potential $V(r)$ of retaining type - $(\lim_{r\to \infty} V(r) = \infty)$ - are obtained in the case of change in the number of states and shift of the energy levels in the spectrum of the radial Schr$\stackrel{..}{o}$dinger equation. In the proposed method, the correction $\Delta V(r)$ as $(r \to \infty)$ is determined from an integral equation of Abelian type, which differs significantly from the standard methods of the inverse problem of quantum mechanics associated with solving the Gel'fand-Levitan equations.