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Clebsch-Gordan series

It is possible to derive some general and useful properties of the rotation matrices from the relationship between the decoupled functions, /i. ti )[/2, 112 and the coupled functions ji,j2, 73. mj), equation (5.79). Operating with R( p, 6, x) on both sets of functions, we obtain  [Pg.157]

If we multiply each side from the left by (/), w 1 j2, rn2 and introduce 3-j symbols, we obtain  [Pg.158]

Now the pairs of rotation matrix products in Eq. (A.7) can be replaced with Clebsch-Gordan series... [Pg.322]

By reexpressing the spherical harmonics in the form of D rotation matrices they may be effectively substituted by a Clebsch-Gordan series yielding... [Pg.323]

The Clebsch-Gordan series for S0(4) can then be simply constructed and is given by... [Pg.214]

The integral over the Euler angles in Eq. (32) is found analytically using the Clebsch-Gordan series [40, 64, 68]... [Pg.519]

P14.21 Use the Clebsch-Gordan series [Chapter 101 to compound the two resultant angular momenta, and impose the conservation of angular momentum on the composite system. [Pg.292]

This is the coupled representation. For a given combination of ji and j2 the possible values of the resultant angular momentum quantum number j are given by the Clebsch-Gordan series... [Pg.361]

See other pages where Clebsch-Gordan series is mentioned: [Pg.214]    [Pg.209]    [Pg.577]    [Pg.49]    [Pg.157]    [Pg.213]    [Pg.189]    [Pg.6]    [Pg.189]    [Pg.157]    [Pg.205]    [Pg.415]   
See also in sourсe #XX -- [ Pg.209 , Pg.277 , Pg.385 ]

See also in sourсe #XX -- [ Pg.157 ]

See also in sourсe #XX -- [ Pg.157 ]

See also in sourсe #XX -- [ Pg.361 ]



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Clebsch-Gordan

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