Convergent perturbation studies in screened coulomb potential systems: a high precision numerical algorithm via Laguerre basis set

In this work, a high precision algorithm is developed to determine the discrete spectrum of screened coulomb potential systems. The algorithm is mainly based upon the use of the perturbation of a hydrogen-like operator by a bounded operator. The Laguerre basis set expansion is employed in the procedure to obtain the operator inversion. Although a functional analytic analysis of errors and proof of convergence theorem are still lacking, it appears, numerically, that the method rapidly converges for bounded screened coulomb potential. Extremely accurate numerical results for the bound-state energies, in the case of Yukawa potential, are presented for illustrative purposes.