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The number state method is used to study soliton bands for three anharmonic quantum lattices: (i) The discrete nonlinear Schrödinger equation, (ii) The Ablowitz-Ladik system, and (iii) A fermionic polaron model. Each of these systems is assumed to have f-fold translational symmetry in one spatial dimension, where f is the number of freedoms (lattice points). At the second quantum level (n = 2) we calculate exact eigenfunctions and energies of pure quantum states, from which we determine binding energy (Eb) effective mass (m*) and maximum group velocity (Vm) of the soliton bands a functions of the anharmonicity in the limit f --> infinity. For arbitrary values of n we have asymptotic expressions for Eb, m*, and Vm as functions of the anharmonicity in the limits of large and small anharmonicity. Using these expressions we discuss and describe wave packets of pure eigenstates that correspond to classical solitons.
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