Classical and Quantum Behavior of Genaralized Oscillators - action variable, angle variable and quantum phase -

TL;DR

This paper explores the relationship between action variables, angle variables, and quantum phases in generalized oscillators, introducing a new Hamilton-Jacobi picture to clarify quantum-mechanical interpretations.

Contribution

It introduces the Hamilton-Jacobi picture of quantum mechanics and clarifies the connection between classical and quantum variables in generalized oscillators.

Findings

Clarification of quantum-mechanical meaning of Hamilton-Jacobi equation

Introduction of the Hamilton-Jacobi picture of quantum mechanics

Insights into the relation among action, angle, and phase variables

Abstract

The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the classical Hamilton-Jacobi equation and related matters is clarified, where a new picture of quantum mechanics is introduced, to be called the Hamilton-Jacobi picture.