Hamilton-Jacobi theory and the relativistic action variable

Abstract

The relativistic quantum Hamilton-Jacobi equations, which are physically equivalent to the relativistic Schrödinger and the Dirac equations, are postulated by extending the recent Leacock-Padgett theory to the relativistic case. Then the relativistic quantum action variables are obtained to show that the exact bound state energy levels of a relativistic system may be determined more conveniently by these variables without solving the dynamical equations.