Generalized Heisenberg relation and Quantum Harmonic Oscillators

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. Electronic address: [email protected] PACS 02.20.Sv, 02.40.Gh, 03.65.Ca, 03.65. − w, 03.70 + k Typeset using REVTEX 1