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本文首先通过对波失星直接乘积的分析指出,如果 *K″∈*K?*K′,则波矢峯Gk″可以有下面四种情况:A)Gk同Gk′,是Gk″的子峯,B)Gk=Gk′=Gk″,C)Gk″=Gs, D)Gs是Gk″的子峯。根据上述四种情况,分别考虑积分A=μ″i″(k″)|fμi(k)|fμ′i′(k′)>的简约。并且证明,对所有四种情况,积分A的值均可由短阵U的矩阵元统一地表达出来。矩阵U是使可约表示Г′简约的转换矩阵,对四种情况,可约表示Г′分别是:A)(Гki?Гk′i′)(?),B)Гi?Гk′i′,C)Гki(s)?Гk′i′(s),D)(Гki(s)?Гk′i′(s))(?)。最后,利用准投影算符的方法,对矩阵U进行了计算,导出空间峯Wigner-Eckart定理的表式。It is shown that in the direct product of two wave vector stars k?k′, if k"∈k?k′, the wave vector group, Gk", may belong to any one of the following cases: A) Both Gk and Gk′ are subgroups of Gk"; B) Gk=Gk′= Gk"; C) Gk" = Gs; D) Gs is the subgroup of Gk". The reduction of an integral A=μ″i″(k″)|fμi(k)|fμ′i′(k′)>, is then studied for each of the four cases. It is found that for all cases, the value of the integral can be expressed in terms of the matrix element of a transformed matrix U by which the reducible representation has been reduced. The corresponding reducible representations Г′s are respec-tively: A) (Гki?Гk′i′)(?);B)Гki?Гk′i′;C)Гki(s)?Гk′i′(s); and D)(Гki(s)?Гk′i′(s))(?). The final form of the integral is then obtained by finding the explicit form of the transformation matrix by using the pseudo-projection operator.
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