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.
Highlights
In 1924 the physicist Max Born put forward for the first time the name “quantum mechanics” in the literature [1]
We present a prescription for obtaining the quantum Hamilton–Jacobi equation from the classical one
We have studied classical and quantum solutions for harmonic oscillator-like systems, further encompassing the driven case and with resonances as well, by using the Hamilton–Jacobi method
Summary
In 1924 the physicist Max Born put forward for the first time the name “quantum mechanics” in the literature [1]. Dirac independently formulated a consistent algebraic framework for quantum mechanics [5], where the equations were obtained with no use of matrix theory It was only in 1926 that the Schrödinger formalism (SF) appeared in the literature. Much has been learned regarding the QHJF in recent years, when several developments have been accomplished in the literature These include the definability of time parameterization of trajectories [27], corrections for any soliton equation for which action–angle variables are known [28], lattice theories [29], gauge invariance in loop quantum cosmology [30], treatment of the relativistic double ring-shaped Kratzer potential [31], shape-invariant potentials in higher dimensions [32], application to the photodissociation dynamics of NOCl [33], and Dirac–Klein–Gordon systems [34].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
