Analogy Between Quantum Mechanics and Optics

Jaume Masoliver A, Ana Ros Camacho

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 Schrödinger'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.

Ángel S. Sanz, Salvador Miret-Artés

A. V. Andrade-Neto, B P Carneiro, J C Rios +1 more

Abstract In this paper we explore the analogies between optical physics and quantum mechanics. The formal similarity between the Helmholtz wave equation and the time-independent Schrödinger equation is presented. Details of the analogy between plane interface and potential step and between thin film and potential barrier are developed and a detailed discussion is provided to reinforce the analogy. We hope that the present work can be useful for undergraduate students.

D. I. Blokhint︠s︡ev

Qian Shang-Wu

By comparison between equations of motion of geometrical optics(GO)and that of classical statistical mechanics(CSM),we find that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM).Furthermore,by comparison between the classical limit(CL)of quantum mechanics(QM)and CSM,we find that CL of QM is CSM not CM,hence we demonstrate that QM is a natural generalization of CSM instead of CM.