Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations

Details Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations

2007-12-13

arxiv.org/abs/0712.2078v1

Physics

Quantum Physics

Scientific paper

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 Schr\"odinger equation of the model. The approach can be generalized to the $D$-dimensional oscillator with non-commuting coordinates.

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