Abstract:%e investigate the validity of the Fourier transformations that have long been used to transform a given Hamiltonian written in configuration space into momentum space. We show that although these transformations are valid for ideal (perfect) lattices, their use for lattices with vacancies poses mathematical problems and renders inaccuracies in the form of the Hamiltonian by not conserving the number of degrees of freedom in the Hilbert space. Consequently, transformations that avoid this problem are found. %'… Show more
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