We study a doubly discrete quantum sine-Gordon equation, which is derived from the quantum Volterra model solved by Faddeev and Volkov [Teor. Mat. Fiz. 92 (1992) 207]. The discrete quantum pendulum is obtained as the simplest special case. The eigenfunctions of its Hamiltonian, displayed as densities on the phase space, are very localized around the classical energy levels.
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