The one-dimensional harmonic oscillator damped with Caldirola-Kanai Hamiltonian

Authors

  • Francis Segovia-Chaves Facultad de Ciencias Exactas y Naturales Universidad Surcolombiana, Huila-Colombia

DOI:

https://doi.org/10.31349/RevMexFisE.64.47

Keywords:

Hamilton-Jacobi equations, Caldirola-Kanai Hamiltonian, damped harmonic oscillator

Abstract

In this paper, the solution to the Hamilton-Jacobi equation for the one-dimensional harmonic oscillator damped with the Caldirola-Kanai model is presented. Making use of a canonical transformation, we calculate the Hamilton characteristic function. It was found that the position of the oscillator shows an exponential decay similar to that of the oscillator with damping where the decay is more pronounced when increasing the damping constant γ. It is shown that when γ = 0, the behavior is of an oscillator with simple harmonic motion. However, unlike the damped harmonic oscillator where the linear momentum decays with time, in the case of the oscillator with the Caldirola-Kanai
Hamiltonian, the momentum increases as time increases due to an exponential growth of the mass m(t) = meγt.

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Published

2018-04-10

How to Cite

[1]
F. Segovia-Chaves, “The one-dimensional harmonic oscillator damped with Caldirola-Kanai Hamiltonian”, Rev. Mex. Fis. E, vol. 64, no. 1 Jan-Jun, pp. 47–51, Apr. 2018.

Issue

Vol. 64 No. 1 Jan-Jun (2018): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2018 Francis Segovia-Chaves

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.