| Issue |
ESAIM: M2AN
Volume 58, Number 6, November-December 2024
Special issue - To commemorate Assyr Abdulle
|
|
|---|---|---|
| Page(s) | 2155 - 2186 | |
| DOI | https://doi.org/10.1051/m2an/2024001 | |
| Published online | 04 December 2024 | |
Discrete quantum harmonic oscillator and Kravchuk transform*
1
INRIA Lille, Univ. Lille & Laboratoire Paul Painlevé, CNRS UMR 8524 Lille, Cité Scientifique, 59655 Villeneuve-d’Ascq, France
2
INRIA Rennes, Univ. Rennes & Institut de Recherche Mathématiques de Rennes, CNRS UMR 6625 Rennes, Campus Beaulieu, 35042 Rennes Cedex, France
** Corresponding author: erwan.faou@inria.fr
Received:
24
April
2023
Accepted:
31
December
2023
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the almost second-order convergence of these discrete functions towards Hermite functions, uniformly for large numbers of modes. We then describe an efficient way to simulate these eigenfunctions and the corresponding transformation. We finally show some numerical experiments corroborating our different results.
Mathematics Subject Classification: 65Q10 / 35Q41 / 41A10
Key words: Harmonic oscillator / Kravchuk polynomials / geometric numerical integration
© The authors. Published by EDP Sciences, SMAI 2024
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