Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations

2007/12/13 by K. Gemba, Gemba, K., Z. T. Hlousek +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.0712.2078

arxiv created 2007/12/13 · arxiv updated 2009/12/01

Abstract

In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infinite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrödinger equation of the model. The approach can be generalized to the D-dimensional oscillator with non-commuting coordinates.

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