  In this paper we revise the main aspects of the Hamiltonian analogy: the fact
that optical paths are completely analogous to mechanical trajectories. We
follow Schr\"{o}dinger's original idea and go beyond this analogy by changing
over from the Hamilton's principal function $S$ to the wave function $\Psi$. We
thus travel from classical to quantum mechanics through optics.

History and Philosophy of Physics;Physics Education