Fock similarity transformation of the electronic Hamiltonian.

Abstract

The covariance of the one-electron Schrödinger equation in a gauge transformation of electromagnetic potentials is customarily discussed, introducing the relationships that describe their changes, induced by a generating function of position coordinates and time, together with a phase transformation of the wavefunction, according to a proposal by Fock, i.e.,2 relying on three distinct hypotheses. The present note shows that (i) a single similarity transformation employing the Fock phase factor is sufficient to prove the covariance of the wave equation and (ii) the Fock transformations of the nonperturbed Hamiltonian ĥ(0) and of the time-derivative operator determine the changes appearing in first and second-order Hamiltonians, ĥ(1) and ĥ(2), a single term being obtained by Fock-transforming ĥ(1).