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A simple sum formula for Clebsch-Gordan coefficients

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Abstract

I derive a simple identity involving a sum of Clebsch-Gordan coefficients with zero magnetic quantum numbers.

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References

  1. Din, A.M. and Zakrzewski, W.J., Nucl. Phys. B168, 173 (1980).

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  2. I thank Drs. M. Kibler and D. Wyler for their interest in this point.

  3. Varshalovitch, D.A., Moskalev, A.N., and Khersonski, V.K., Quantum Theory of Angular Momentum (Russian edition), Nauka, 1975.

  4. Gradstein, I.S. and Ryshik, I.M., Higher Transcendental Functions, Vol. I, McGraw-Hill, 1953.

  5. I thank Dr. R. Askey for pointing out that the integral can, in fact, be evaluated for general parameters using a generalized version of Dougall's formula.

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  1. LAPP, Annecy-le-Vieux, France

    A. M. Din

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  1. A. M. Din
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Din, A.M. A simple sum formula for Clebsch-Gordan coefficients. Lett Math Phys 5, 207–211 (1981). https://doi.org/10.1007/BF00420700

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  • DOI: https://doi.org/10.1007/BF00420700

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