Solution
= Solution
$E_0(k)=\hbar^2k^2/(2m)$. Periodic boundary conditions give $k=2πn/L$. Orthogonality of plane waves gives $\langle k|U|k\prime\rangle=U_l$ when $k\prime-k=2πl/a$, and zero otherwise.
= Solution
$E_0(k)=\hbar^2k^2/(2m)$. Periodic boundary conditions give $k=2πn/L$. Orthogonality of plane waves gives $\langle k|U|k\prime\rangle=U_l$ when $k\prime-k=2πl/a$, and zero otherwise.