An algebraic approach to a charged particle in a uniform magnetic field

Authors

  • D. Ojeda-Guillén Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, C.P. 07738, Ciudad de México, Mexico.
  • M. Salazar-Ramírez Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, C.P. 07738, Ciudad de México, Mexico.
  • R.D. Mota Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, 04430, Ciudad de México, Mexico.
  • V.D. Granados Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Col. Zacatenco, C.P. 07738, Ciudad de México, México.

DOI:

https://doi.org/10.31349/RevMexFisE.64.127

Keywords:

Coherent states, group theory, Landau levels.

Abstract

We study the problem of a charged particle in a uniform magnetic field with two different gauges, known as Landau and symmetric gauges. By using a similarity transformation in terms of the displacement operator we show that, for the Landau gauge, the eigenfunctions for this problem are the harmonic oscillator number coherent states. In the symmetric gauge, we calculate the SU(1; 1) Perelomov number coherent states for this problem in cylindrical coordinates in a closed form. Finally, we show that these Perelomov number coherent states are related to the harmonic oscillator number coherent states by the contraction of the SU(1; 1) group to the Heisenberg-Weyl group.

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Published

2018-06-11

How to Cite

[1]
D. Ojeda-Guillén, M. Salazar-Ramírez, R. Mota, and V. Granados, “An algebraic approach to a charged particle in a uniform magnetic field”, Rev. Mex. Fis. E, vol. 64, no. 2 Jul-Dec, pp. 127–132, Jun. 2018.

Issue

Vol. 64 No. 2 Jul-Dec (2018): Revista Mexicana de Física E

Section

02 Education in Physics

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.