We have seen in Sec. II A that the original many-body Schrödinger equation ( ) can be reduced to a one-body equation involving effective vector and scalar potentials [Eq. ( )], whose solution is the marginal amplitude, χ. However, the scalar and vector potentials appearing in Eq. ( ) are functionals of the conditional amplitude, Φ. It seems then appropriate to look at the equation satisfied by the conditional amplitude. By simply substituting Eqs. ( ) and (4) into Eq. ( ), after some rearrangements, one gets: