Quantum Hamilton-Jacobi Formalism

Abstract

AbstractThe quantum Hamilton-Jacobi (QHJ) formalism is one of the independent formalisms of quantum mechanics ( Styer et al in Am. J. Phys. 70, 288-297, 2002 [1]), whose roots lie in the esoteric formulation of classical mechanics, namely the Hamilton-Jacobi theory (Goldstein in Classical Mechanics. Pearson Education India, 2002; Rana and Joag in Classical Mechanics. Tata McGraw-Hill, 1991 [2, 3]. The latter is intimately connected to the canonical transformation theory, whose development led to the action-angle formulation of classical mechanics. This form of classical dynamics played an important role in the development of quantum mechanics through the Bohr-Sommerfeld quantization rule and its relativistic version.