  The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's
Principle predicted by several theories of Quantum Gravity. It consists of a
modified commutator between position and momentum. In this work we compute
potentially observable effects that GUP implies for the harmonic oscillator,
coherent and squeezed states in Quantum Mechanics. In particular, we rigorously
analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new
operators that act as ladder operators on the perturbed states. We use these
operators to define the new coherent and squeezed states. We comment on
potential applications.
