4.1. Using the nearly free-electron approximation for a one-dimensional (1-D)crystal lattice and assuming that the only nonvanishing Fourier coefficientsof the crystal potential are v(n/a) and v(-π/a) in (4.73), show that near theband edge at k = 0, the dependence of electron energy on the wave vectork is given bywhere m* =Ekelectron at k = 0.= Eo += mo[1 − (32m²aª / hªлª)v(π/a)²]¯¹ is the effective mass of theħ²k²2m*

To start, let's recall the nearly free-electron approximation for a 1-D crystal lattice. In this…

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