We study a doubly discrete quantum sine-Gordon equation, which is deri
ved 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, d
isplayed as densities on the phase space, are very localized around th
e classical energy levels.