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Consider the one-dimensional periodic potential (with X > 0) V(x) = X Σ δ(x-ja). j=0,±1, +2... ħ2² (a) Derive the disper
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Consider the one-dimensional periodic potential (with X > 0) V(x) = X Σ δ(x-ja). j=0,±1, +2... ħ2² (a) Derive the disper
Consider the one-dimensional periodic potential (with X > 0) V(x) = X Σ δ(x-ja). j=0,±1, +2... ħ2² (a) Derive the dispersion relation cos(ka) = cos(ka) + sin(ka). (b) Plot the right-hand side of this relation for m Xa/ħ² = 3π/2 and indicate the resulting allowed energy bands. Show that the upper band edges are located at ka = n with integer n = = 1, 2,....
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