Calculating helium atomic excited states in coordinate space

Abstract

Two coupled Schrödinger equations are used to calculate excited states of atomic helium. Using product state functions for the two-electron state, the shooting method is used to numerically determine the energies of the allowed singlet and triplet levels. The calculations agree well with the data, and the coordinate-space basis yields Schrödinger equations for helium that are familiar to students who have used similar methods for the hydrogen atom.