The logarithmic perturbation theory for bound states in spherical-symmetric potentials via the $\hbar$-expansions

Dobrovolska, I. V.; Tutik, R. S.

The logarithmic perturbation theory for bound states in spherical-symmetric potentials via the $\hbar$-expansions

Authors

Description

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As examples, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator and the Debye potential are considered.
Talk given at International School-Seminar "New physics and QCD at external conditions" (Dniepropetrovsk, Ukraine, May 3-6, 2007); 11 pages; prepared for publication in Proceedings