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 Schrödinger equation H ψ = E ψ is reduced to a Schrödinger 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 .