Quantization and the Classical Hamilton-Jacobi Equation

Abstract

In this paper, a formalism for quantization is developed which starts out from the Hamilton-Jacobi expression, $\frac{\partial S}{\partial t}+H(\frac{\partial S}{\partial q}, q)$, and which leads to its usual quantum-mechanical operator equivalent by means of straightforward algebra. The quantum-mechanical operator equivalents of $H$ and $p$ are then seen to be the consequence of assigning a number of equally probable classical paths to a dynamical system.