9780030839931, Chapter 9, Problem 3P

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Chapter 9, Problem 3P Problem Effect of Weak Periodic Potential at Places in k-Space Where Bragg Planes Meet Consider the point W (kw = 0)) in the Brillouin zone of the fee structure shown (see Figure 9.14). Here three Bragg planes ((200), (111), meet, and accordingly the free electron energies = k - 2π (1, 1, 1) 2 , 2 (9.45) = k (1, 1, 1) , a 2 degenerate when k = kw, and equal to EW = h2kw2/2m Figure 9.14 First Brillouin zone for a face-centered cubic crystal. (111) U W (200) (a) Show that in a region of k-space near W, the first-order energies are given by solutions to where U2 = U200, U1 = = U and that at W the roots are = &w - U₂ & = + (9.46) (b) Using a similar method, show that the energies at the point U (kU = 1. 1) ) are = = + + (9.47) where = Step-by-step solution There is no solution to this problem yet. Get help from a Chegg subject expert. Ask an expert