Prove the statements (10.2.7) and (10.2.8), and that the other terms vanish as stated, by explicitly evaluating the matrix elements, using the band functions in (1.13.9) and (1.13.10), and substituting Φ_x = x, Φ_y = y, Φ_z = z, and Φ_s = 1.

Show also that the term α_n is real for these states, because the factor i that appears in (10.2.9) cancels an i that occurs in the matrix elements.

Transcribed Image Text:

<호, +를pyls, +호), (10.2.7)