Perturbed crystals in thekqrepresentation. II. Orthonormal localized states

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Abstract
An orthonormal set of localized states for a crystal with a perturbation is developed. It includes the impurity problem, surface states, superlattices, and other perturbations. These localized states are used for deriving one-band effective Hamiltonians up to second order of the perturbation expansion. Relatively simple results for localized states and one-band Hamiltonians are obtained in the cases of wide and narrow energy-gap crystals. The orthonormal set of states that diagonalize the Hamiltonian is also used for deriving an expression for local charge densities in a perturbed crystal which can directly be compared with experiment.