ONE DIMENSIONAL BAND THEORY IN WKB APPROXIMATION

We consider the one-dimensional Schroedinger equation with a periodic potential in the WKB approximation. The bounded solutions correspond to energies E which satisfy the condition |(1/ T(E)) cos Φ | ≤ 1 where T(E) is transmission coefficient of a potential hill; 2h {combining short solidus overlay}Φ(E) is the classical action within one potential well evaluated between the classical turning points if E ≤ Vmax, or evaluated for one period of the potential if E ≥ Vmax; μ(E) is the phase shift of the wave transmitted across one potential hill. A detailed discussion is given concerning the nature of the band spectrum, the dispersion curve, and the effective mass. The same method is used to discuss finite periodic systems and the associated surface states. © 1969.