This form is perhaps more familiar and leads one to identify A(r) as a magnetic-like vector potential. Indeed, equation for the marginal amplitude is formally equivalent to a Schrödinger equation for a one-body quantum system (such as the hydrogen atom) subject to an external magnetic field. However, A(r), along with the scalar potential in parenthesis in the RHS of Eq. ( ), encodes the effect of the conditional amplitude and, thus, of the remaining N -1 electrons on the reference one.