Excited state wave functions

Wave functions and energies were calculated for the 2s, 3p ₀, and 4d ₀ states of the hydrogen atom using the Messmer and Rayleigh-Ritz variational methods with minimization of the second eigenvalue. The wave functions were linear expansions of Gaussian functions and both linear and exponential parameters were varied. Except for the two term expansions, calculated values of the energies and expectation values, r ^–1, r and r ² were within two percent of the true values for both methods.