One-dimensional classical dynamics with maximal length uncertainty

Abstract

We calculated equations of motion describing a classical dynamics with Lawson's maximal length uncertainty formalism. We obtained an exact analytical solution for the free particle case and derived differential equations for position X and momentum P with respect to time t that are easily solvable by numerical integration for any potential V. Using the 4^th order Runge-Kutta method, the time evolution of a particle's position and momentum subjected to linear potential, harmonic oscillator potential, and sinusoidal potential are plotted. Finally, we have determined that the phase space trajectory of a particle with maximal length uncertainty subjected to any potential is invariant of the existence of maximal length uncertainty.