The Relation between Quantum Mechanics, Classical Mechanics and Optics

Daniela Dragoman

DETLEF GLOGE, Dietrich Marcuse

It is shown that the relation between ray optics and wave optics is analogous to the relation between the classical mechanics of a point particle and quantum mechanics. The time coordinate of quantum mechanics has to be replaced with a length coordinate and the light wavelength λ takes the place of Planck’s constant h. A well-known result of quantum mechanics is that it coincides with classical mechanics in the limit h → 0. Correspondingly, wave and ray optics must coincide in the limit λ → 0.

Ángel S. Sanz, Salvador Miret-Artés

Marco Di Mauro, A. Drago, Adele Naddeo

Abstract Classical and quantum mechanics are two very different theories, each describing the world within its own range of validity. It is often stated that classical mechanics emerges from quantum mechanics in a certain limit. This is known as the correspondence principle. According to Planck’s version of the correspondence principle, classical mechanics is recovered when the limit in which a dimensionless parameter containing Planck’s constant h goes to zero is taken, while Bohr’s version entails taking the limit of large quantum numbers. However, despite what is usually stated in textbooks, the relation between the two theories is much more complex to state and understand. Here we deal with this issue by analysing some key examples, in some of which also the analogously subtle relation between wave and geometric optics is considered. Implications for quantum mechanics teaching at undergraduate level are carefully discussed.

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.