Two types of electronic states in one-dimensional crystals of finite length

Exact and general results on the electronic states in one-dimensional crystals bounded at tau and tau + L, where L = Na, N is a positive integer, and a is the potential period, are presented. Corresponding to each energy band of the Bloch wave, there are N - 1 states in the finite crystal whose energies are dependent on L but not on tau and map the energy band exactly. There is always one and only one electronic state corresponding to each band gap of the Bloch wave, whose energy is dependent on r but not on L. This state is either a constant-energy confined band-edge state or a surface state in the band gap. (C) 2002 Elsevier Science (USA).