Spherical geometry, Zernike’s separability, and interbasis expansion coefficients

DOI10.1063/1.5099974zbMath1441.33007OpenAlexW2977279321MaRDI QIDQ5205157

Natig M. Atakishiyev, Kurt Bernardo Wolf, George S. Pogosyan, Alexander Yakhno

Publication date: 10 December 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5099974

zbMATH Keywords

Laplace-Beltrami operatorhyperspherical harmonicsZernike polynomialsZernike systemfree motion on \(S^3\)Lie algebra \(so(4)\)

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Diffraction, scattering (78A45) Series solutions to PDEs (35C10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Waves and radiation in optics and electromagnetic theory (78A40) Compactifications; symmetric and spherical varieties (14M27)

Related Items (4)

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system ⋮ On the generalization of classical Zernike system ⋮ Zernike System Stems from Free Motion on the 3-Sphere ⋮ New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates

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