To obtain an effective equation for the marginal amplitude, χ, let us apply Eqs. ( ) and (4) to Eq. ( ), then left-multiply by Φ * m and integrate over all variables but r. The nabla operator acting on the factorized wavefunction of Eq. ( ) makes extra terms appear compared to the usual (Schrödinger-equation-like) expression. Note that, from the PNC, it follows that