Exactly solvable dynamical models with a minimal length uncertainty
Abstract
We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that a minimal length increases the speed of a free particle and the rate of fall of a particle that is subject to the influence of a linear potential. Our results suggest that the characteristic frequency of systems tend to increase when there is a minimal length. This is a common feature that we observed for the oscillator systems that we have considered.
Keywords
Cite
@article{arxiv.1602.02240,
title = {Exactly solvable dynamical models with a minimal length uncertainty},
author = {Reginald Christian Bernardo and Jose Perico Esguerra},
journal= {arXiv preprint arXiv:1602.02240},
year = {2016}
}
Comments
This is a version of the manuscript (10 pages) submitted to Few-Body Systems on 16 December 2014. A revised version has been accepted by Few-Body Systems on 9 April 2015