Relating problems in two dimensions. A particle in a uniform magnetic field and a free particle

Authors

DOI:

https://doi.org/10.31349/RevMexFis.72.010701

Keywords:

Schrödinger equation, equivalence of Lagrangians, free particle, particle in a uniform magnetic field

Abstract

We give a coordinate transformation in the extended configuration space that maps the trajectories of a free particle in two dimensions into the trajectories of a charged particle in a uniform magnetic field. We show that this coordinate transformation also relates the solutions of the Schrödinger equations for these two problems.

References

G.F. Torres del Castillo, Relating the free particle with the harmonic oscillator, Rev. Mex. Fís. 71 (2025) (to appear).

G.F. Torres del Castillo, An Introduction to Hamiltonian Mechanics (Springer, Cham, 2018), sec. 2.4. https://doi.org/10.1007/978-3-319-95225-3.

D.J. Griffiths, Introduction to Quantum Mechanics, 2nd. ed. (Pearson Prentice Hall, Upper Saddle River, NJ, 2005), Prob. 2.22.

G.F. Torres del Castillo and L.A. Capulín Tlaltecatl, Applications of the complex, double and dual numbers in Lagrangian mechanics, Rev. Mex. Fís. 69 (2023) 010702. https://doi.org/10.31349/RevMexFis.69.010702.

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Published

2026-01-01

How to Cite

[1]
G. F. Torres del Castillo, “Relating problems in two dimensions. A particle in a uniform magnetic field and a free particle”, Rev. Mex. Fís., vol. 72, no. 1 Jan-Feb, pp. 010701 1–, Jan. 2026.

Issue

Vol. 72 No. 1 Jan-Feb (2026): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

License

Copyright (c) 2026 G. F. Torres del Castillo

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