Dynamics of Electrons in Solids in External Fields. II

Further applications of the $\mathrm{kq}$ representation to the dynamics of electrons in solids are carried out. The Bloch theory of conduction electrons is reformulated in the new representation. The symmetry of the problem is discussed in light of the $\mathrm{kq}$ representation. In particular, the motion of an electron in both a periodic potential and a constant magnetic field is developed on a firm quantum-mechanical basis. A complete and orthonormal set of magnetic Bloch functions is defined. These functions are shown to obey the magnetic translation symmetry, and it is for this reason that they are very useful in describing the motion of a Bloch electron in a magnetic field.