Generalized Heisenberg relation and Quantum Harmonic Oscillators

Details Generalized Heisenberg relation and Quantum Harmonic Oscillators Generalized Heisenberg relation and Quantum Harmonic Oscillators

2006-10-10

arxiv.org/abs/quant-ph/0610079v1

Physics

Quantum Physics

10 pages, LaTeX

Scientific paper

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.

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