Modular pairs of some second order q-difference equations are considered.
These equations may be interpreted as a quantum mechanics of a sort of
hyperelliptic pendulum. It is shown the quantization of a spectrum may be
provided by the condition of the analyticity of the wave function. Baxter's t-Q
equations for the quantum relativistic Toda chain in the ``strong coupling
regime'' are related to the system considered, and the quantization condition
for Q-operator is also considered.Comment: 11 pages, LaTeX2
