When possible, we will drop the R, t dependence of the matrix elements, eigenvalues, and eigenvectors to avoid notation clutter. The eigenvector |v 1 (R, t)⟩ is normalized to one and it is defined up to a phase. The electronic density operator is R, t-dependent and so is this phase. The N -1 eigenvectors |v m̸ =1 ⟩ with λ 2 = 0, can be chosen arbitrarily, as long as