For an optical transition in a crystal with T_d symmetry between a valence band with Γ₈ symmetry and a conduction band with Γ₆ symmetry, which states are coupled to each other by left-circular and right-circular polarized light along the zaxis? To answer this, use the Wigner–Eckart theorem; you can use either Table 6.9 or the symmetry tables at the website associated with this book.

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Table 6.9 Coupling coefficients for the outer product I'5 T6 in the Ta group [w]) |w₂) (wo) |w₂) |wd) -i/√6 0 0 i/ √2 1/√/6 0 0 -i/√3 |us)|vo) |us)|vo) -i/√3 0 |us)|v) 0 1/√/3 |u)|v) -1/√3 0 |u)|v) i/√3 0 0 |u)|v2) 0 -i/√3 i√√2/√3 0 -1/√/2 0 0 -i/√2 0 -1/√/2 0 0 0 0 i/√6 0 1/√6 i√2/√3 0