Editing Computational implementation of integral equations
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*[http://dx.doi.org/10.1016/0010-4655(70)90034-2 Taro Tamura "Angular momentum coupling coefficients", Computer Physics Communications '''1''' pp. 337-342 (1970)] | *[http://dx.doi.org/10.1016/0010-4655(70)90034-2 Taro Tamura "Angular momentum coupling coefficients", Computer Physics Communications '''1''' pp. 337-342 (1970)] | ||
*[http://dx.doi.org/10.1016/0010-4655(71)90030-0 J. G. Wills "On the evaluation of angular momentum coupling coefficients", omputer Physics Communications '''2''' pp. 381-382 (1971)] | *[http://dx.doi.org/10.1016/0010-4655(71)90030-0 J. G. Wills "On the evaluation of angular momentum coupling coefficients", omputer Physics Communications '''2''' pp. 381-382 (1971)] | ||
==Clebsch-Gordon coefficients and Racah's formula== | |||
The Clebsch-Gordon coefficients are defined by | |||
:<math>\Psi_{JM}= \sum_{M=M_1 + M_2} C_{M_1 M_2}^J \Psi_{M_1 M_2},</math> | |||
where <math>J \equiv J_1 + J_2</math> and satisfies <math>(j_1j_2m_1m_2|j_1j_2m)=0</math> | |||
for <math>m_1+m_2\neq m</math>. | |||
They are used to integrate products of three spherical harmonics (for example the addition of | |||
angular momenta). | |||
The Clebsch-Gordan coefficients are sometimes expressed using the related Racah V-coefficients, | |||
<math>V(j_1j_2j;m_1m_2m)</math> | |||
(See also the [[Racah W-coefficients]], sometimes simply called the Racah coefficients). | |||
*[http://dx.doi.org/10.1016/0010-4655(74)90059-9 Robert E. Beck and Bernard Kolman "Racah's outer multiplicity formula", Computer Physics Communications '''8''' pp. 95-100 (1974)] | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1080/00268977900102861 M. J. Gillan "A new method of solving the liquid structure integral equations" Molecular Physics '''38''' pp. 1781-1794 (1979)] | #[http://dx.doi.org/10.1080/00268977900102861 M. J. Gillan "A new method of solving the liquid structure integral equations" Molecular Physics '''38''' pp. 1781-1794 (1979)] |