Addition of a large number of identical angular momenta. Statistical distributions

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Abstract
The quantum mechanical addition of an arbitrary (very large) number of identical angular momenta is considered. The resulting states jm usually occur many times. The corresponding multiplicities Pj and Qm are investigated. Several explicit formulae for Qm are given. The asymptotic approximations for multiplicities Pj and Qm, which are the Wigner and Gauss distributions respectively, are derived. All parameters of the distributions are explicitly obtained. A comparison of theoretical multiplicities with the exact ones is made when the number of angular moments is relatively small.

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