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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT 256 37 "Computing Energy Bands in Problem 8.6" }}{PARA 0 "" 0 "
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" 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "H:
=<<-1/2,1/2,1/2*exp(3*I*k)>|<1/2,1,1/2>|<1/2*exp(-3*I*k),1/2,-1/2>>;" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "eq:=CharacteristicPolynom
ial(H,E)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(%*8
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "eq1:=x^3-6*x-4*(cos(3
*k/2))^2=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "eigenenergy:
=[solve(eq1,x)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "E_1:=k-
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>eigenenergy[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "E_3:=k-
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E_1(k)/2,E_2(k)/2,E_3(k)/2],k=0..2*Pi/3,color=[red,blue,green],thickne
ss=3,axes=boxed,title=\"Energy Bands in Problem 8.6\",labels=[\"k\",\"
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257 "" 0 "" {TEXT 257 7 "THE END" }}}}{MARK "14" 0 }{VIEWOPTS 1 1 0 1 
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