Chapter 7 #1

Chapter 7 #4

(b) The band gap at zone boundary plane normal to the end of reciprocal lattice

vector is 2 times the Fourier component . From part (a), we

know this quantity equals to 0 for first order approximation. So the band gap is zero to

the first order approximation.

xa

A ˆ2π

=

r

AU r

2

Chapter 7 #6

Additional problem

)cos(4a

bm

a

Aπ=

)cos(4a

bm

a

Aπ=