From Classical to Quantum Mechanics through Optics

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 $\mathrm{\Psi }$. We thus travel from classical to quantum mechanics through optics.