Transition energies for excited states of helium: An evaluation of two simple approximation techniques

Abstract

Two standard approximation techniques are applied to the problem of calculating the transition energies of the 3-2 lines in the helium spectrum. First-order perturbation theory gives very poor results, in some cases inverting the order. A simple one-parameter variational calculation, on the other hand, gives results that are remarkably accurate. A comparison of these results gives insight into the nature of both approximations. These calculations can be performed mostly analytically, with the help of a symbolic algebra computer program, and are well within the reach of upper-division undergraduates in an elementary quantum mechanics course.