Abstract
This chapter illustrates several uses of crystal Clebsch–Gordan coefficients. These coefficients provide an efficient and straightforward method for calculating the independent elements of tensors, such as those arising in effective Hamiltonian theory and in Raman scattering. Clebsch–Gordan coefficients were first used for calculating the symmetry of matrix elements of rotation group operators. These are used to simplify the calculation of scattering tensors. The elements of the electric-field-induced Raman tensor are given as linear combinations of the elements for the intrinsic first-order Raman tensor, and the coefficients of these linear combinations are again Clebsch-Gordan coefficients.
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