To conclude, in this work, we have discussed the exact factorization formalism for the static Schrödinger equation of a purely electronic system and for a general eigenstate, introducing generalized local potentials v kin and v N -1 which could in principle serve the description of excited states within density-functional theorie(s). Our definitions presume the gauge choice of real positive marginal wavefunction, which however has the remarkable advantage that the electronic vector potential A, stemming from the fact that the wavefunction is complex [Eq. ( )], is related in a straightforward way to the current density [Eq. ( )].