PERTURBATIVE EVALUATION OF THE EIGENVALUES OF THE HERBST-HAMILTONIAN

We reconsider the well-known and long-debated problem of the calculation of the eigenvalues of the Herbst Hamiltonian 2 root p(2)+m(2)-kappa/r. We give a formulation of the problem that allows, for the first time, a perturbative evaluation of the eigenvalues for any n and l, and in principle up to any order in kappa via standard Kato perturbation theory, We present the evaluation of the energy of the n = 1 and n = 2 states up to kappa(6), confirming the result previously obtained by Le Yaouanc et al, with a completely different technique. Moreover we give the n = 2, l = 1 level, which is new, Discussion of the results and comparison with previous findings are given at the end.