24 this derivative does not vanish at these values of

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Unformatted text preview: k = nπ/a, where n = 0,1,2,…. From (3.5), we know that and then we can take the derivative of (3.24) as At k = nπ/a, the RHS vanishes, but the LHS is the derivative of the LHS of (3.24). This derivative does not vanish at these values of ka, so we must have 3.9 Using the parameters in problem 3.5 for a free electron and letting a = 0.42 nm, determine the width (in eV) of the allowed energy bands that exist for (a) 0 < ka < π, and (b) π < ka < 2π. From problem 3.5, we can find the energy...
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