Harmonic potential as an effective limit of a discrete classical interaction

Abstract

Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is traced with gravity for stressing the relevance of such discrete interaction models.

Typo corrections and 4 references added. To appear in J. of Physics A: Math. and Gen