Group theoretic approach to the screened Coulomb problem

Perturbation method based on the group theory is developed for the radial solution of the Schrödinger equation with screened Coulomb potential. It may be treated as an alternative to the analytic perturbation theory proposed recently by McEnnan, Kissel, and Pratt (Phys. Rev. A, 2 (1976), 532) and is based on the expansion of the potential of the following form $\text{V(r) = ?(}\text{a}\text{r}\text{) × (1 + λV}{}_1\text{r + λ}{}^2\text{V}{}_2\text{r}{}^2\text{+ …)}$. Corrections to the point-Coulomb energy levels are given as series in λ and also the screened Coulomb eigenstates are given in the form of expansions in powers of λ. The method is applied also to the continuous spectrum and similar expansions are found. The problem of the normalization of both discrete and continuous spectrum eigenstates is discussed and we find some differences in the case of the scattering states. Origin of this discrepancy is explained.