Energy levels of the laser-dressed Coulomb potential by the potential envelope method

Abstract

The method of potential envelopes is employed to approximate the bound-state energies of the Schrodinger Hamiltonian, - Delta - upsilon /(r2+ lambda 2)12/. It is shown that the simple formula E=minr>0(P2/r2- upsilon /(r2+ lambda 2)12/) provides upper bounds to the energies if P=(2n+l-1/2) and lower bounds when P=(n+l), with accurate values found by direct numerical integration.