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Unformatted text preview: EEE 539Spring 2008 Homework 5 3.5 Plot the function f( a)=9sin( a)/ a+cos( a) a 6 . Also, given the function f( a)=cos(ka), indicate the allowed values of a which will satisfy this equation. 2 2 4 6 8 10 5 10 15 20 f( a) a Allowed regions2 2 4 6 8 10 5 10 15 20 f( a) a Allowed regions 3.7 Using equation (3.24), show that dE/dk=0 at k=n /a, where n=0,1,2,. Equation (3.24) is given as ka a a a P cos cos sin = + , and (3.5) relates the energy to . m E 2 2 2 h = Now, let us take the derivative of (3.24) with respect to , as ka a k a a a a a P sin sin sin cos 2 = . When k = n /a (n an integer), the righthand side is zero. Since, in general, the term in the brackets is nonzero, we must have = k in order to satisfy the equation. Then, . = = k E dk dE 3.14 Two possible valence bands are shown in the E versus k diagram given in Fig. Two possible valence bands are shown in the E versus k diagram given in Fig....
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 Spring '08
 Ferry

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