Existence of a minimal measurable length and an upper bound for the momentum fluc- tuations are the casting reasons for generalization of uncertainty principle and then refor- mulation 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 its energy eigenstates and energy spectrum. Investiga- tion of coherent states for a generalized harmonic oscillator and its generic behavior are the other topics in our study.
