Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations

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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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Quantum Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/144131

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.2078
 http://arxiv.org/abs/0712.2078

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arXiv