Relating the free particle with the harmonic oscillator

Authors

DOI:

https://doi.org/10.31349/RevMexFis.71.030701

Keywords:

Harmonic oscillator, Schrödinger equation, Hamilton-Jacobi equation

Abstract

We show that by means of a coordinate transformation in the extended configuration space the problem of a free particle can be related to that of a harmonic oscillator in classical mechanics and in quantum mechanics.

References

G.F. Torres del Castillo, An Introduction to Hamiltonian Mechanics (Springer, Cham, 2018). Sec. 6.4. https://doi.org/10.1007/978-3-319-95225-3

G.F. Torres del Castillo, op. cit. Sec. 2.4

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

R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965, reprinted by Dover, New York, 2010). Sec. 8-1.

G.S. Pogosyan, L.E. Vicent y K.B. Wolf, El l´ımite del oscilador cuantico a la partícula libre, Rev. Mex. Fís. E 51 (2005) 18.

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Published

2025-05-01

How to Cite

[1]
G. F. Torres del Castillo, “Relating the free particle with the harmonic oscillator”, Rev. Mex. Fís., vol. 71, no. 3 May-Jun, pp. 030701 1–, May 2025.

Issue

Vol. 71 No. 3 May-Jun (2025): Revista Mexicana de Física

Section

07 Gravitation, Mathematical Physics and Field Theory

License

Copyright (c) 2025 Gerardo Francisco Torres del Castillo

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