Conditional probability amplitudes in wave mechanics

The total wave function of a system ψ(x, y) is expressed as a product of a marginal amplitude function f(y) and a conditional amplitude function ϕ(x | y). The original Schrodinger equation Hψ = Eψ is reduced to a Schrodinger equation for the marginal amplitude H′f = Ef. The factorization of ψ is in principle exact. It achieves a partial separation of the variables x and y.