Using the same order-of-magnitude approximation as the previous exercise, estimate the typical coefficient (k(vector)) that gives the

Using the same order-of-magnitude approximation as the previous exercise, estimate the typical coefficient β(k(vector)) that gives the fraction of opposite spin, according to (10.9.6). Assume that the nearby state mixed in is about 0.1 eV away, and take the other parameters from the previous exercise. Is there an appreciable fraction of opposite spin mixed in, for k around one-tenth of the Brillouin zone?

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|i') = \i) + ħ² 4m² c² j#i k. (jo x VU\i) E₁ - Ej -(j), (10.9.6)