Finite optical Hamiltonian systems

Wolf, Kurt Bernardo; Atakishiyev, Natig M.; Vincent, Luis Edgar; Krötzsch, Guillermo; Rueda-Paz, Juvenal

doi:10.1117/12.902162

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2014

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“…In particular, discrete (finite) quantum oscillator models, which are constructed in terms of these polynomials of the hypergeometric type, find a large number of applications in signal [4,5,7] and in optical image processing [8,20]. Recall that, chronologically, this type of discrete oscillator models were introduced in the following way.…”

Section: Introductionmentioning

confidence: 99%

Kravchuk polynomials and irreducible representations of the rotation group $$SO(3)$$ S O ( 3 )

Atakishiyeva

Atakishiyev

Wolf

2014

Bol. Soc. Mat. Mex.

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We set forth that the Kravchuk polynomials of a discrete variable are actually "encoded" within appropriate finite-dimensional irreducible representations of the group of rotations of three-dimensional space SO(3). Hence, discrete irreducible representation spaces of the group SO(3) can be naturally interpreted as finite (discrete) versions of the linear quantum harmonic oscillator. Mathematics Subject Classification

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Section: Introductionmentioning

confidence: 99%