Simulation of Gaussian wave packets used to illustrate elementary quantum mechanics scenarios

Authors

  • F. Guzmán-Cajica FCFM-UMSNH
  • Francisco S. Guzmán Murillo IFM-UMSNH

DOI:

https://doi.org/10.31349/RevMexFisE.21.020219

Keywords:

Self-gravitating systems; dark matter; bose condensates

Abstract

In this paper we numerically solve the time dependent Schrödinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet in a harmonic oscillator potential with non-trivial initial conditions in one and two dimensions, which is compared with their classical analogs to show how Ehrenfest theorem holds. We also include simulations of the diffraction through the single and double slit potentials, the refraction with a step potential and the dispersion by a central potential. The aim of this paper is to illustrate with simulations, nowadays easy to implement, scenarios that can help explaining the basics of the wave-particle duality.

References

Time-dependent Schrödinger equation, https://servicio-social.gitbook.io/computational-physics/time-dependent-schrodinger-equation

M. A. Reyes A. Fernández Téllez D. M. Reyna-Muñoz, On the quantum problem with harmonic, stark, coulombian and centrifugal barrier potential terms, and biconfluent heun functions, Rev. Mex. Fis. E 21, (2024) 010209 https://doi.org/10.31349/RevMexFisE.21.010209

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics, A Wiley - Interscience publication v. 1 (Wiley, 1977)

F. S. Guzmán, Numerical Methods for Initial Value Problems in Physics, 1st ed. (Springer, 2023)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, 2007)

G. Gamow, El Nuevo Breviario Del Señor Tompkins, 2nd ed. (Fondo de Cultura Económica, 2012)

G. Gamow and M. Edwards, The New World of Mr Tompkins: George Gamows Classic Mr Tompkins in Paperback, edited by Bozhe-WuTranslator Stannard, RussellEditor (Cambridge University Press, 1999)

E. Hecht, Optics (Pearson, 2012)

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Published

2024-07-01

How to Cite

[1]
F. Guzmán-Cajica and F. S. Guzmán Murillo, “Simulation of Gaussian wave packets used to illustrate elementary quantum mechanics scenarios”, Rev. Mex. Fis. E, vol. 21, no. 2 Jul-Dec, pp. 020219 1–, Jul. 2024.

Issue

Vol. 21 No. 2 Jul-Dec (2024): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2024 F. Guzmán-Cajica, Francisco S. Guzmán Murillo

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.