Abstract
Systems that stem from projection of free motion on a manifold are the best candidates to exhibit remarkable symmetry properties. This is the case of free motion on the 3-sphere which, properly projected on the 2-dimensional manifold of a disk, yields the Zernike system. This exhibits separability in a variety of coordinate systems, polynomial solutions, and interbasis expansion coefficients that are special Clebsch–Gordan coefficients and Hahn orthogonal polynomials.
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Acknowledgements
N.M.A. and K.B.W. thanks project AG-100119 awarded by the Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México. A.Y. thanks the support of project pro-sni-2019 (Universidad de Guadalajara).
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Wolf, K.B., Atakishiyev, N.M., Pogosyan, G.S., Yakhno, A. (2021). Zernike System Stems from Free Motion on the 3-Sphere. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_16
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