Problems 4.1. 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(7/a) and v(-n/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 Ek = Eo + 2m* where m* = mo[l – (32mža*/h*n*)v(7/a)²]¬l is the effective mass of the electron at k = 0. %3D - %3D 4.2. The E-k relation of a simple cubic lattice given by (4.79) is derived from the tight-binding approximation. Show that near k 0 this relation can be expressed by ħ?k? Ek = Eno + 2m* where m* = h2 /2B,a². And for k 7/a, show that the E-k relation is given by Ek = Eno + 2m* where m* = %3D
Problems 4.1. 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(7/a) and v(-n/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 Ek = Eo + 2m* where m* = mo[l – (32mža*/h*n*)v(7/a)²]¬l is the effective mass of the electron at k = 0. %3D - %3D 4.2. The E-k relation of a simple cubic lattice given by (4.79) is derived from the tight-binding approximation. Show that near k 0 this relation can be expressed by ħ?k? Ek = Eno + 2m* where m* = h2 /2B,a². And for k 7/a, show that the E-k relation is given by Ek = Eno + 2m* where m* = %3D
Principles of Instrumental Analysis
7th Edition
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Chapter12: Atomic X-ray Spectrometry
Section: Chapter Questions
Problem 12.10QAP
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