Abstract
The hyperincursive algorithm for the discrete harmonic oscillator is
perfectly stable and energy conserving. By identifying the natural
parameters of the system, we transform the algorithm into a normal
formalism based on dynamic equations of motion. We find that the
simultaneous difference equations of motion are complex, that the natural
parameters are classical analogues of the quantum mechanical creation and
annihilation operators, and that the solution is of utmost simplicity. The
methodology is applicable to any dynamical system, has conceptual
importance for discrete physics, and practical utility for numerical
simulations.
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