Perturbed crystals in thekqrepresentation: III. The uniform magnetic field

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Abstract
The symmetric coordinates in solids are used for developing Wannier functions in the presence of a uniform magnetic field. The functions are shown to form an orthonormal set with respect to different bands and different sites of the crystal. A simple relation is established between the eigenfunctions of a Bloch electron in a magnetic field and the newly developed Wannier functions. This relation is used for an entirely elementary derivation of one-band effective Hamiltonians. Multiband operators are defined in the space of envelope functions for different physical quantities, e.g., the radius vector, velocity, and acceleration.