  Existence of a minimal measurable length and an upper bound for the momentum
fluctuations are the casting reasons for generalization of uncertainty
principle and then reformulation of Hilbert space representation of quantum
mechanics. In this paper, we study the consequences of the Generalized
Uncertainty Principle (GUP) in the presence of both minimal length and maximal
momentum. We consider a simple harmonic oscillator in the framework of GUP by
introducing it's energy eigenstates and energy spectrum. Investigation of
coherent states for a generalized harmonic oscillator and it's generic behavior
are the other topics in our study.
