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The Harmonic Oscillator via the Discrete Path Approach

Adel F. Antippa and Daniel M. Dubois

p. 141-153

    Abstract

    The discrete path approach has recently been use to obtain a closed form solution for two simultaneous difference equations with variable coefficients. We apply this result to the solution of the discretized harmonic oscillator and recover the well known traditional solutions. In the process we learn how the enumerative discrete path solution transforms into a more convenient compact analytic closed form. The discrete path approach is specially adapted to problems with mixed boundary conditions like those arising in the modeling of anticipatory systems.

    Index

    Keywords

    discrete path, closed form solution, difference equations, harmonic oscillator, anticipatory systems

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    References

    Bibliographical reference

    Adel F. Antippa and Daniel M. Dubois, « The Harmonic Oscillator via the Discrete Path Approach », CASYS, 11 | 2002, 141-153.

    Electronic reference

    Adel F. Antippa and Daniel M. Dubois, « The Harmonic Oscillator via the Discrete Path Approach », CASYS [Online], 11 | 2002, Online since 12 July 2024, connection on 27 December 2024. URL : http://popups.uliege.be/3041-539x/index.php?id=1471

    Authors

    Adel F. Antippa

    Département de Physique, Université du Québec à Trois-Rivières, Trois-Rivières, Québec, Canada,G9A 5H7

    Daniel M. Dubois

    Centre for Hyperincursion and Anticipation in Ordered Systems, CHAOS asbl, Institut de Mathématique, B37, Université de Liège, Grande Traverse 12, B-4000 Liège 1, Belgique

    By this author

    Copyright

    CC BY-SA 4.0 Deed