Equations ( ) and are interesting in that they bring to light a local relationship between the modulus and the phase of the conditional amplitude. In particular, in the equation for the modulus [Eq. ( )], it is interesting to notice that the square of the gradient of the phase of the conditional amplitude acts as an extra scalar potential term in the N -electron Hamiltonian; while in the equation for the phase [Eq. ] there is a compensation between the Laplacian of the phase and the "coupling" between this latter and the modulus of the conditional wavefunction. This can also be seen directly from the total wavefunction, expressed in polar representation with its modulus R Ψ and phase θ as done in Eq. ( ) for the conditional amplitude, i.e.: