DKH Transformation of One-Electron Terms

To consider the effect of the DKH transformation on the many-electron Hamiltonian of Eq. (12.63), the Hilbert space formulation of many-particle quantum mechanics presented in section 8.4 needs to be recalled. 

The innermost or initial transformation of the sequence of Eqs. (11.15) and (12.1), i.e., the free-particle Foldy-Wouthuysen transformation, reads in the N-electron case 

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