Interbasis expansions for the isotropic 3D harmonic oscillator and bivariate Krawtchouk polynomials

An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible representations of SO(3) on the energy eigenspaces of the three-di...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2014-01, Vol.47 (2), p.25202-13
Main Authors: Genest, Vincent X, Vinet, Luc, Zhedanov, Alexei
Format: Article
Language:English
Subjects:
Cartesian
Clebsch-Gordan coefficients
Decomposition
dual Hahn polynomials
harmonic oscillator
Harmonic oscillators
interbasis expansions
Lie groups
Mathematical analysis
multivariate Krawtchouk polynomials
Polynomials
Representations
rotation group
Three dimensional
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Summary:An explicit expression for the general bivariate Krawtchouk polynomials is obtained in terms of the standard Krawtchouk and dual Hahn polynomials. The bivariate Krawtchouk polynomials occur as matrix elements of the unitary reducible representations of SO(3) on the energy eigenspaces of the three-dimensional isotropic harmonic oscillator and the explicit formula is obtained from the decomposition of these representations into their irreducible components. The decomposition entails expanding the Cartesian basis states in the spherical bases that span irreducible SO(3) representations. The overlap coefficients are obtained from the Clebsch-Gordan problem for the Lie algebra.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/2/025202