  In this work, the dynamics of the deformed one-dimensional harmonic
oscillator with minimal length uncertainty is examined and the analytical
solutions for time evolution of position and momentum operators are presented
in which the rough approximation that neglects the higher order terms in
BakerHausdor lemma is avoided. Based on these analytical solutions the
uncertainties for position and momentum operators are calculated in a coherent
state, and an unexpected squeezing effect in both coordinate and momentum
directions is found in comparison with ordinary harmonic oscillator. Obviously
such a squeezing effect is induced by the minimal length uncertainty
(gravitational effects). Our results are applied to the electrons trapped in
strong magnetic fields to examine the degree of the existing squeezing effect
in a real system, which shows the squeezing degree induced by minimal length
uncertainty is very small.
