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Details for article 8 of 9 found articles
| Title: |
The discrete and periodic heat and harmonic oscillator equation |
| Author: |
Hilger, Stefan |
| Appeared in: |
Journal of difference equations and applications |
| Paging: | Volume 13 (2007) nr. 8-9 pages 741-793 |
| Year: |
2007-08 |
| Contents: |
In this paper we present a generalization of the famous Dirac ladder formalism for the Schrodinger harmonic oscillator equation. Whereas the classical one-dimensional harmonic oscillator [image omitted] acts on functions of a real continuous variable, our generalization works within the framework of Pontryagin dual groups, the discrete group h and the circle group h- 1 ( unit circle). We will define so-called Hermite-Kravchuk operators that constitute a close connection between the heat and harmonic oscillator equation that is invisible in the real continuous case. This generalization is not only the result of a crude discretization or perturbation process. Since this theory preserves and expands the beautiful algebraic background, one can speak of a structural discretization or “periodization”. We hope that this theory will also serve as a model for physical phenomena. |
| Publisher: |
Taylor & Francis |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 8 of 9 found articles
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