On the nonrelativistic limit of the Dirac hamiltonian

In this paper, by a systematic use of the reduction scheme for the analytic perturbation of pseudoresolvents, the nonrelativistic limit of the Dirac Hamiltonian is reconsidered. The main results are: the 1/c 4 ― correction to the bound states energies in the degenerate case and the 1/c 2 ― correction to the scattering amplitude. The relation of the Foldy-Wouthuysen transformation with the reduction scheme, and with the relativistic corrections that we derived is discussed On considere le probleme de la limite non relativiste de l'hamiltonien de Dirac, en utilisant des pseudo-resolvantes. Les resultats principaux qu'on obtient sont: la correction en 1/c 4 pour les energies des etats stationnaires dans le cas degenere et la correction en 1/c 2 pour l'amplitude de diffusion. On discute aussi la relation de la transformee de Foldy-Wouthuysen avec le schema de reduction et les corrections calculees

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