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Spectra and eigenfunctions of discrete Hamiltonians are computed using algebraic, analytic, and numerical tools. In particular, we consider the Hofstadter and the Second Neighbor Square Lattice model, the Triangular Lattice model in an inhomogenous magnetic field, the Doubly-discrete Quantum Pendulum, and the Honeycomb model. Qualitative properties of the spectra are related to symmetries. Semiclassical analysis in the algebraic setting for the Doubly-discrete Quantum Pendulum is shown to match numerical results well. The connection to integrable models is mentioned.
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Kreft et al. (1996) studied this question.
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