In the semiconductor GaAs, the valence band states at zone center are split by spin–orbit interaction into four degenerate states

where the states |1〉, |0〉, and | − 1〉 are the Bloch spatial cell functions with p-symmetry, and | ↓〉 and | ↑〉 are the pure spin states. The spin- 3/2 states are “heavy-hole” states and the spin- 1/2 states are the “light-hole” states. The conduction the band states are pure spin states. Determine the electron–hole exchange splitting of exciton states made from electrons and holes in these two bands.

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| + ³) = -|1)| 1) 1 1 + / -) = - 12 = 1 =|1)| ↓) - /3 - (一) 3) = -1)| ↓), 2 今 1〉| ↑〉 + =10)| ↑) 3 =10)| ↓) (10.8.47)