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Using the nearly free-electron approximation for a one-dimensional (1-D) crystal lattice and assuming that the only nonvanishing Fourier coefficients of the crystal potential are v(n/a) and v(-7/a) in (4.73), show that near the band edge at k = 0, the dependence of electron energy on the wave vector k is given by ħ²k² 2m*' Ek = Eo + where m* = mo[1 - (32m²a/h*n*)v(n/a)²-¹ is the effective mass of the electron at k = 0.

Using the nearly free-electron approximation for a one-dimensional (1-D) crystal lattice and assuming that the only nonvanishing Fourier coefficients of the crystal potential are v(n/a) and v(-7/a) in (4.73), show that near the band edge at k = 0, the dependence of electron energy on the wave vector k is given by ħ²k² 2m*' Ek = Eo + where m* = mo[1 - (32m²a/h*n*)v(n/a)²-¹ is the effective mass of the electron at k = 0.

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Using the nearly free-electron approximation for a one-dimensional (1-D) crystal lattice and assuming that the only nonvanishing Fourier coefficients of the crystal potential are v(n/a) and v(-7/a) in (4.73), show that near the band edge at k = 0, the dependence of electron energy on the wave vector k is given by ħ²k² 2m*' Ek = Eo + where m* = mo[1 - (32ma/h*n*)v(n/a)2-¹ is the effective mass of the electron at k = 0.
Transcribed Image Text:Using the nearly free-electron approximation for a one-dimensional (1-D) crystal lattice and assuming that the only nonvanishing Fourier coefficients of the crystal potential are v(n/a) and v(-7/a) in (4.73), show that near the band edge at k = 0, the dependence of electron energy on the wave vector k is given by ħ²k² 2m*' Ek = Eo + where m* = mo[1 - (32ma/h*n*)v(n/a)2-¹ is the effective mass of the electron at k = 0.
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