In the limit n → ∞, this becomes a functional integral, which, apart from a nonessential factor, is directly the product of the probability amplitudes ⟨ x b, t b | x a, t a ⟩ (more precisely, since one must work with a continuous spectrum, the respective densities) to find the quantum mechanical particle at t a in the initial state x a and at t b in the final state x b.