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

Abstract

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 periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.

Accepted for publication in Brazilian Journal of Physics

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Cited by in corpus (6)

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• Minimal Length Effects on Chaotic Motion of Particles around Black Hole Horizon
• The Classical Limit of Minimal Length Uncertainty Relation:Revisit with the Hamilton-Jacobi Method
• On deformations of classical mechanics due to Planck-scale physics
• Chaotic Motion around a Black Hole under Minimal Length Effects
• Minimal Length Effects on Motion of a Particle in Rindler Space