  In this paper dynamics and quantum mechanical coherent states of a simple
harmonic oscillator are considered in the framework of Generalized Uncertainty
Principle(GUP). Equations of motion for simple harmonic oscillator are derived
and some of their new implications are discussed. Then coherent states of
harmonic oscillator in the case of GUP are compared with relative situation in
ordinary quantum mechanics. It is shown that in the framework of GUP there is
no considerable difference in definition of coherent states relative to
ordinary quantum mechanics. But, considering expectation values and variances
of some operators, based on quantum gravitational arguments one concludes that
although it is possible to have complete coherency and vanishing broadening in
usual quantum mechanics, gravitational induced uncertainty destroys complete
coherency in quantum gravity and it is not possible to have a monochromatic ray
in principle.
