A note on coherent states with quantum gravity effects

• Consequences of the Generalized Uncertainty Principle (GUP) in the presence of both minimal length and maximal momentum.
• Consideration of a simple harmonic oscillator in the framework of GUP by introducing its energy eigenstates and energy spectrum.
• Investigation of coherent states for a generalized harmonic oscillator and its generic behavior.

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 its energy eigenstates and energy spectrum. Investigation of coherent states for a generalized harmonic oscillator and its generic behavior are the other topics in our study.