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Algebraic Solution of the Harmonic Oscillator With Minimal Length Uncertainty Relations

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 نشر من قبل Zvonimir Hlousek
 تاريخ النشر 2007
  مجال البحث فيزياء
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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 Schrodinger equation of the model. The approach can be generalized to the $D$-dimensional oscillator with non-commuting coordinates.



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