Simple perturbation and perturbation-variation treatments of the 1sσg and 2pσu states of H

First-order wave functions and binding energies of the 1sσ_g and 2pσ_u states of H are calculated by simple methods for internuclear separations between 0.2 and 10_a0. An exact perturbation treatment of the lsσ_g state with a zeroth-order function of the form N exp (-sRλ/2) exp (sR μ2) yields only fair results. An alternative method starts with zeroth-order functions of the form N exp (-sRλ/2)[exp (-sRμ/2) ± exp (sRμ/2)] for the 1 and 2 states, respectively. An approximate first-order trial function is set up and the energies are determined variationally. For both states the results are comparable to those obtained by exact perturbation treatments of the same order.