Kravchuk oscillator revisited

The study of irreducible representations of Lie algebras and groups has traditionally considered their action on functions of a continuous manifold (e.g. the 'rotation' Lie algebra so(3) on functions on the sphere). Here we argue that functions of a discrete variable -Kravchuk functions- a...

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Published inJournal of physics. Conference series Vol. 512; no. 1; pp. 12031 - 8
Main Authors Atakishiyeva, Mesuma K, Atakishiyev, Natig M, Wolf, Kurt Bernardo
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2014
Subjects
Algebra
Continuity (mathematics)
Group theory
Harmonic oscillators
Lie groups
Manifolds
Mathematical models
Oscillators
Physics
Representations
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Summary:The study of irreducible representations of Lie algebras and groups has traditionally considered their action on functions of a continuous manifold (e.g. the 'rotation' Lie algebra so(3) on functions on the sphere). Here we argue that functions of a discrete variable -Kravchuk functions- are on equal footing for that study in the case of so(3). They lead to a discrete quantum model of the harmonic oscillator, and offer a corresponding set of special function relations. The technique is applicable to other special function families of a discrete variable, which stem from low-dimensional Lie algebras and are stationary solutions for the corresponding discrete quantum models.
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ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/512/1/012031