A geodesical approach for the harmonic oscillator

Authors

  • Rodrigo Sánchez-Martínez Universidad Veracruzana
  • Alvaro Lorenzo Salas-Brito Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Unidad Azcapotzalco
  • Hilda Noemí Núñez-Yépez Departamento de Fı́sica, Universidad Autónoma Metropolitana, Unidad Iztapalapa

DOI:

https://doi.org/10.31349/RevMexFisE.17.6

Keywords:

Harmonic Oscillator, Mathematical Physics, Hamiltonian Mechanics, Canonical Transformations, Free Particle.

Abstract

The harmonic oscillator (HO) is present in all contemporary physics, from elementary classical mechanics
to quantum field theory. It is useful in general to exemplify techniques in theoretical physics. In this work,
we use a method for solving classical mechanic problems by first transforming them to a free particle form
and using the new canonical coordinates to reparametrize its phase space. This technique has been used to
solve the one-dimensional hydrogen atom and also to solve for the motion of a particle in a dipolar potential.
Using canonical transformations we convert the HO Hamiltonian to a free particle form which becomes
trivial to solve. Our approach may be helpful to exemplify how canonical transformations may be used in
mechanics. Besides, we expect it will help students to grasp what they mean when it is said that a problem
has been transformed into another completely different one. As, for example, when the Kepler problem is
transformed into free (geodesic) motion on a spherical surface.

Author Biography

Rodrigo Sánchez-Martínez, Universidad Veracruzana

Graduate Student at the Facultad de Física of the Universidad Veracruzana

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Published

2020-01-28

How to Cite

[1]
R. Sánchez-Martínez, A. L. Salas-Brito, and H. N. Núñez-Yépez, “A geodesical approach for the harmonic oscillator”, Rev. Mex. Fis. E, vol. 17, no. 1 Jan-Jun, pp. 6–10, Jan. 2020.

Issue

Vol. 17 No. 1 Jan-Jun (2020): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2020 Rodrigo Sánchez-Martínez, Alvaro Lorenzo Salas-Brito, Hilda Noemí Núñez-Yépez

Creative Commons License

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.