Finite differences, Clebsch-Gordan coefficients, and hypergeometric functions (in Russian)
The generalization of the angular momentum theory is proposed, which uses as its generating representation the representation of finite generalized hypergeometric series by means of operators of finite differences and symbolic powers. A number of new relations is obtained, which generaiize the conception of the coupling (the addition) of angular momenta; in particular, the expression of the Racah coefficient through the sum of products of the two Clebsch--Gordan coefficients is found. The effectivity of the finite difference method is demonstrated and the finite-difference differentiation and integration of the Clebsch- Gordan coefficients and j-symbols over angular momenta and their projections is considered. The formula obtained by the method presented directly give the numerical values for the j-symbols and other quantities of the angular momentum theory.
- Research Organization:
- Inst. of World Economics and International Relations, Moscow
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-29-006288
- OSTI ID:
- 4397826
- Journal Information:
- Theoretical and Mathematical Physics, Journal Name: Theoretical and Mathematical Physics Journal Issue: 1 Vol. 17; ISSN 0040-5779
- Country of Publication:
- Country unknown/Code not available
- Language:
- Russian
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