The wave function TCr) of the electrons in the crystal lattice is expressed by the well-known Bloch's theorem:where the function U k (r) has the period of the crystal lattice such mat U k (r)=U k (r+T) (here T is any vector of the Bravais lattice). The nearly free-electron approximation is a good standing point for discussing the energy band theory. It explains the origin of the band gap and that of the effective mass m* which is defined as the reciprocal of the curvature of E (energy) versus k (wavevector) diagram. The functional dependence of E on k for the various bands, E"(k), is defined by the Schrodinger equation:HT(r) = _EL + V(r) = E^r) (7.2) 2m* where p 2 /2m* is the kinetic energy (p=-ihV), V(r) is the potential energy, and E is the energy eigenvalue. Since the electrons in the crystal are influenced by the periodic potential, the electron mass m* used in Eq. (7.2) differs largely from the free electron mass m<, (see Chapter 8).The reciprocal space, also called phase space, k-space, and momentum space, is a convenient tool to describe the behavior of both vibrational states and electronic states. The coordinate axes of the reciprocal lattice are the wavevectors of the plane waves corresponding to the vibrational modes (Section 5.