Variational solution of Schrödinger's equation for the static screened Coulomb potential

Abstract
A variational method is used to obtain solutions to Schrödinger's equation for a particle in a static screened Coulomb potential. Energy eigenvalues are obtained for the lowest 45 states. The analytic wave functions generated by this method are used to obtain the probabilities for spontaneous emission in the dipole approximation as a function of screening length, for transitions between the six lowest states.