On the Hamilton-Jacobi method in classical and quantum nonconservative systems

TL;DR

This paper extends Hamilton-Jacobi solutions to nonconservative classical oscillatory systems and their quantum analogs, demonstrating the formalism's effectiveness and proposing experimental applications in magnetic resonance.

Contribution

It provides complete solutions for quantum Hamilton-Jacobi equations in nonconservative systems and applies these to magnetic field problems, bridging classical and quantum mechanics.

Findings

Complete solutions for quantum Hamilton-Jacobi equations in specific systems

Analytical results demonstrating the power of the quantum Hamilton-Jacobi formalism

Proposal to use NMR techniques for experimental validation

Abstract

In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In addition, we get the solution of the quantum Hamilton-Jacobi equation for an electric charge in an oscillating pulsing magnetic field. We also argue that for the case where a charged particle is under the action of an oscillating magnetic field, one can apply nuclear magnetic resonance techniques in order to find experimental results regarding this problem. We obtain all results analytically, showing that the quantum Hamilton-Jacobi formalism is a powerful tool to describe quantum mechanics.