#### DOCUMENTA MATHEMATICA, Vol. 7 (2002), 167-182

Raymond Brummelhuis, Heinz Siedentop, and Edgardo Stockmeyer

The Ground State Energy of Relativistic One-Electron Atoms According to Jansen and Heß

Jansen and Heß -- correcting an earlier paper of Douglas and Kroll -- have derived a (pseudo-)relativistic energy expression which is very successful in describing heavy atoms. It is an approximate no-pair Hamiltonian in the Furry picture. We show that their energy in the one-particle Coulomb case, and thus the resulting self-adjoint Hamiltonian and its spectrum, is bounded from below for $\alpha Z\leq 1.006$.

2000 Mathematics Subject Classification: 81Q10, 81V45

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