Abstract
Using properties of the Shannon and Tsallis entropies, we obtain new inequalities for the Clebsch–Gordan coefficients of the group SU(2). For this, we use squares of the Clebsch–Gordan coefficients as probability distributions. The obtained relations are new characteristics of correlations in a quantum system of two spins. We also find new inequalities for Hahn polynomials and the hypergeometric functions 3F2.
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The research of V. I. Manko was supported by the Tomsk State University Competitiveness Improvement Program.
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 193, No. 2, pp. 356–366, November, 2017.
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Chernega, V.N., Manko, O.V., Manko, V.I. et al. New information-entropic relations for Clebsch–Gordan coefficients. Theor Math Phys 193, 1715–1724 (2017). https://doi.org/10.1134/S0040577917110113
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DOI: https://doi.org/10.1134/S0040577917110113