  The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump
are well understood in the regime of weak and intermediate Josephson coupling,
i.e. E_J\lesssim E_C. Instead of perturbative treatment of charging effects,
the present work applies the charge state representation in the the strong
coupling case. From the discrete Hamiltonian we construct effective, truncated
PDE Hamiltonians which yield approximate, but analytical, wave functions and
energies for the ground state. The validity of the expressions is confirmed by
comparing the results against numerically obtained eigenstates and
eigenenergies, whenever possible. For uniform arrays, the results converge
rapidly and even \phi-dependence of the wave function is rather well described.
In the inhomogeneous case we find the Hamiltonian to be parametrically
renormalisable in order to obtain an accurate ground state energy. A method for
for finding an inhomogeneous trial wave function is explained. As a passing
note, we briefly examine the intertwined connection between the pumped charge
and the Berry's phase. As addendum, we have explicitly validated the ground
state ansatz for \phi=0 when N<43.
