From Classical to Quantum Mechanics through Optics

TL;DR

This paper explores the transition from classical to quantum mechanics via optics by extending the Hamiltonian analogy and replacing Hamilton's principal function with the wave function.

Contribution

It introduces a novel perspective on quantum mechanics derivation from optics by moving beyond the classical Hamiltonian analogy using Schrödinger's approach.

Findings

Optical paths are analogous to mechanical trajectories.

Transition from classical to quantum mechanics via optical principles.

Wave function formulation provides a bridge between optics and quantum theory.

Abstract

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.