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Journal of Physics A Mathematical and General

Addition or arbitrary number of identical angular momenta

V V Mihailov

Published Feb 1, 1977• 29 citations
Publisher

Abstract

Under the vector addition of angular momenta, each equal to s, the resulting angular momentaj occur with some multiplicity. The general formula for these multiplicities is obtained by a simple algebraic method. In the case of s=1/2 the expression proves to be a well known one. Also given are some relations connected with the multiplicities.

DOI
10.1088/0305-4470/10/2/003

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Under the vector addition of angular momenta, each equal to s, the resulting angular momentaj occur with some multiplicity. The general formula for these multiplicities is obtained by a simple algebraic method. In the case of s=1/2 the expression proves to be a well known one. Also given are some relations connected with the multiplicities.
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 P j and Q m are investigated. Several explicit formulae for Q m are given. The asymptotic approximations for multiplicities P j and Q m , 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.