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 Schrodinger's original idea and go beyond this analogy by changing over from the Hamilton's principal function S to the wavefunction Ψ. We thus travel from classical to quantum mechanics using optics as a guide. Unfortunately, and despite its mathematical beauty and simplicity, the connection between classical and quantum mechanics through optics is nowadays hardly known and mostly ignored in university education. The present work tries to fill this gap.