Summary: It is shown that the Schrödinger equation can be derived via a variation on the Hamiltonian methods of classical physics that feature the action function \(S\). This variation consists mainly in treating an ensemble of particles instead of a single one. Moreover, the ensemble probability fluid must move in accordance with the laws of a special diffusion process. From the viewpoint adopted here, quantum mechanics is compared with classical mechanics, where the probability fluid of an ensemble is seen to move as a nonviscous laminar flow process.