Next Article in Journal
Numerical Study of Natural Convection Flow of Nanofluid Past a Circular Cone with Cattaneo–Christov Heat and Mass Flux Models
Previous Article in Journal
Generalized Truncation Positive Normal Distribution
Previous Article in Special Issue
A Dynamical System with Random Parameters as a Mathematical Model of Real Phenomena
Open AccessArticle

Discrete Quantum Harmonic Oscillator

1
Faculty of Mathematics, University of Bialystok, Ciołkowskiego 1M, 15-245 Białystok, Poland
2
Physics Department, Cinvestav, AP 14-740, Mexico City 07000, Mexico
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(11), 1362; https://doi.org/10.3390/sym11111362
Received: 1 October 2019 / Revised: 29 October 2019 / Accepted: 31 October 2019 / Published: 3 November 2019
(This article belongs to the Special Issue Differential and Difference Equations and Symmetry)
In this paper, we propose a discrete model for the quantum harmonic oscillator. The eigenfunctions and eigenvalues for the corresponding Schrödinger equation are obtained through the factorization method. It is shown that this problem is also connected with the equation for Meixner polynomials.
Keywords: difference equations; discrete Schrödinger equation; quantum harmonic oscillator; classical discrete orthogonal polynomials; factorization method; Meixner polynomials difference equations; discrete Schrödinger equation; quantum harmonic oscillator; classical discrete orthogonal polynomials; factorization method; Meixner polynomials
MDPI and ACS Style

Dobrogowska, A.; Fernández C., D.J. Discrete Quantum Harmonic Oscillator. Symmetry 2019, 11, 1362.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop