Kravchuk oscillator revisited

8th International Symposium on Quantum Theory and Symmetries

Atakishiyeva, Mesuma K.^1 ; Atakishiyev, Natig M.^2 ; Wolf, Kurt Bernardo^3

Facultad de Ciencias, Universidad Autónoma Del Estado de Morelos, Av. Universidad s/n, Cuernavaca, Morelos 62250, Mexico^1

Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autonoma de México, Av. Universidad s/n, Cuernavaca, Morelos 62250, Mexico^2

Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Av. Universidad s/n, Cuernavaca, Morelos 62250, Mexico^3

关键词: Discrete variables;    Harmonic oscillators;    Irreducible representations;    Low dimensional;    Quantum modeling;    Quantum models;    Special functions;    Stationary solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012031/pdf
DOI  :  10.1088/1742-6596/512/1/012031

来源: IOP

【 摘 要 】

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.