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Details van artikel 8 van 9 gevonden artikelen
| Titel: |
The discrete and periodic heat and harmonic oscillator equation |
| Auteur: |
Hilger, Stefan |
| Verschenen in: |
Journal of difference equations and applications |
| Paginering: | Jaargang 13 (2007) nr. 8-9 pagina's 741-793 |
| Jaar: |
2007-08 |
| Inhoud: |
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. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 8 van 9 gevonden artikelen
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