Energy band The potential is periodic,with the period a,then we may write the general wavefunction as the superposition of energy eigenfunction u_1(x),and u_2(x). W,(x)=Au,(x)+B2(x) 0≤x≤a wn(x)=e"kow(x-a) a≤x≤2a Wu(x)=ekav,(x-a)=ekaLAu (x-a)+Buz(x-a) Au(a)+Buz(a)=e"ka[Au (O+Buz (O] xAu(a)Buz"(a)u)+Bus"Energy band • The potential is periodic, with the period a, then we may write the general wavefunction as the superposition of energy eigenfunction u_1(x), and u_2(x).           a x 2a 0 x a 1 2         x e x a x Au x Bu x iKa II I    x e x a e Au x a Bu x a iKa I iKa  II     1   2                               ' ' ' 0 ' 0 0 0 : 1 2 1 2 1 2 1 2 Au a Bu a e Au Bu Au a Bu a e Au Bu x a iKa iKa