Band Theory, Kittel chapter 7
Band Theory, Kittel chapter 7
Band Theory, Kittel chapter 7
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Kronig-Penney model<br />
for 0 < x < b<br />
ψ ( x) = cos( kx), ψ ( x)<br />
=<br />
1 1 2<br />
for b < x < a<br />
sin( kx<br />
1<br />
)<br />
k<br />
1<br />
k<br />
=<br />
2 mE ( −V1<br />
)<br />
<br />
1 2<br />
ψ<br />
ψ<br />
x k x b kb<br />
k sin( k ( x−b))sin( kb)<br />
1 2 1<br />
1() = cos(<br />
2( − ))cos(<br />
1<br />
) −<br />
,<br />
k2<br />
cos( k ( x−b))sin( kb) sin( k ( x−b))cos( kb)<br />
2 1 2 1<br />
2() x = +<br />
.<br />
k1 k2<br />
k<br />
=<br />
2 mE ( −V2<br />
)<br />
<br />
2 2<br />
Except for the coefficients, these are the same solutions as we found for light<br />
in a layered material.
Change language