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

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.

References in corpus (6)

• Hawking Radiation from Elko Particles Tunnelling across Black Strings Horizon
• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics
• Bekenstein-Hawking entropy in expanding universes from black hole theorems
• Quantum Hamilton-Jacobi Theory
• Energy Quantisation and Time Parameterisation
• Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation