Finite oscillator models: the Hahn oscillator
EI Jafarov, NI Stoilova… - Journal of Physics A …, 2011 - iopscience.iop.org
Journal of Physics A: Mathematical and Theoretical, 2011•iopscience.iop.org
A new model for the finite one-dimensional harmonic oscillator is proposed based upon the
algebra. This algebra is a deformation of the Lie algebra extended by a parity operator, with
the deformation parameter α. A class of irreducible unitary representations of is constructed.
In the finite oscillator model, the (discrete) spectrum of the position operator is determined,
and the position wavefunctions are shown to be dual Hahn polynomials. Plots of these
discrete wavefunctions display interesting properties, similar to those of the parabose …
algebra. This algebra is a deformation of the Lie algebra extended by a parity operator, with
the deformation parameter α. A class of irreducible unitary representations of is constructed.
In the finite oscillator model, the (discrete) spectrum of the position operator is determined,
and the position wavefunctions are shown to be dual Hahn polynomials. Plots of these
discrete wavefunctions display interesting properties, similar to those of the parabose …
Abstract
A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra. This algebra is a deformation of the Lie algebra extended by a parity operator, with the deformation parameter α. A class of irreducible unitary representations of is constructed. In the finite oscillator model, the (discrete) spectrum of the position operator is determined, and the position wavefunctions are shown to be dual Hahn polynomials. Plots of these discrete wavefunctions display interesting properties, similar to those of the parabose oscillator. We show indeed that in the limit, when the dimension of the representations goes to infinity, the discrete wavefunctions tend to the continuous wavefunctions of the parabose oscillator.
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