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

From Classical to Quantum Mechanics through Optics