Irreducible spherical tensors are like spherical harmonics that under rotations transform into one another. A typical irreducible spherical tensor depends on two quantities, usually designated as *k* and *q*, which play a role parallel to *j* and *m* of the angular momentum. The matrix elements of these tensors between different angular momentum states *j*′, *m*′ and *j*, *m* are often quite complicated but ttey can be simplified considerably due to a theorem by Wigner and Eckart. This allows one to separate the matrix element into two factors: one which is just the Clebsch-Gordan coefficient involved in combining *k* with *j* to give *j*′. This is called the geometrical factor and the other is a single term that is ...

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