Perturbative evaluation of the eigenvalues of the Herbst Hamiltonian

Details Perturbative evaluation of the eigenvalues of the Herbst Hamiltonian Perturbative evaluation of the eigenvalues of the Herbst Hamiltonian

1995-05-31

arxiv.org/abs/hep-ph/9505432v2

Phys.Lett. B359 (1995) 133-140; Erratum-ibid. B546 (2002) 305-306

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, Eq. (19) and (22) are corrected; as a consequence the result of Eq. (26) has changed at order alpha^6

Scientific paper

10.1016/S0370-2693(02)02699-0

We reconsider the well-known and long-debated problem of the calculation of the eigenvalues of the Herbst Hamiltonian 2\sqrt{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.

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