The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario

In this work we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore the motion is still periodic with the new period depending on the minimal length. This result is very important since it can be used to probe the Planck-scale physics. We show applications of our results in spectroscopy and gravity.