Gauging away the electron–electron interaction by the local phase of complex wave functions in two-electron systems

The electron-electron interaction is eliminated in the expectation values of the electronic Hamiltonian for two-electron systems. The part of the Hamiltonian referring to the repulsive interaction is gauged away by the local phase of the complex wave functions, much like a gauge eld transformation, thereby leading to a one-electron Hamiltonian. Despite the appearance of complex wave functions, the expectation values of the total momentum operator vanish and Lowdin\u27s criterion holds for the stationary states