53三维周期场中的近自由电子近似及布里渊区.PDF

Brillouin L L3 N a V Na3 r r r r ⋅ ik r r r Blochψ (r ) u (r )e k k r Born-Karmanu r (r ) k ⎧ψr (0,y , z ) ψr (L , y , z ) ⎪ k k i k L x r r ψ (x ,0, z ) ψ (x ,L , z ) e 1 ⎨ k k ⎪ r r ψ (x , y ,0) ψ (x , y ,L) ⎩ k k 2πn 2πn 2πn r k x , k y , k z n , n , n k x L y L z L x y z 3 3 r 8π 8π k V Na 3 r k → → → r 2π 0 r 2π 0 r 2π 0 b1 i , b2 j , b1 k