Comment on relativistic wave equations and negative-energy states

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Abstract
In a recent article [Phys. Rev. A 30, 703 (1984)] Hardekopf and Sucher solve the relativistic wave equation in momentum space for hydrogenlike systems. They find that by surrounding the hydrogenic Hamiltonian with projection operators for free-particle positive-energy states, the ground-state energy is lowered. In this Comment, we investigate this problem in some detail and conclude that the application of unsuitable projection operators will, in fact, introduce negative-energy states to the Hamiltonian of interest rather than remove them. The general considerations lead to the conclusion that in studying single-particle corrections to the wave function in a perturbation expansion, the correct procedure is to include the negative-energy states of the unperturbed Hamiltonian. It is also noted that the use of relativistic Hartree-Fock wave functions will remove to lowest order of perturbation theory the presence of single virtual electron-positron pairs.

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