  In this paper, we consider a system consisting of two capacitively coupled
superconducting islands via Josephson junctions. We show that it can be reduced
to two coupling harmonic oscillators under certain conditions, and solved
exactly in terms of a displacing transformation, a beam-splitter-like
transformation, and a squeezing transformation. It is found that the system
evolves by a rotated-squeezed-coherent state when the system is initially in a
coherent state. Quantum dynamics of the Cooper pairs in the two superconducting
islands is investigated. It is shown that the number of the Cooper pairs in the
two islands evolves periodically.
