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 {A figure is presented}. 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 κ via standard Kato perturbation theory. We present the evaluation of the energy of the n = 1 and n = 2 states up to κ⁶, 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.