  We study the consequences of the generalized Heisenberg uncertainty relation
which admits a minimal uncertainty in length such as the case in a theory of
quantum gravity. In particular, the theory of quantum harmonic oscillators
arising from such a generalized uncertainty relation is examined. We
demonstrate that all the standard properties of the quantum harmonic
oscillators prevail when we employ a generalized momentum. We also show that
quantum electrodynamics and coherent photon states can be described in the
familiar standard manner despite the generalized uncertainty principle.
