The Quantum Josephson Hamiltonian In The Phase Representation
  The quantum Josephson Hamiltonian of two weakly linked Bose-Einstein condensates is written in an overcomplete phase representation, thus avoiding the problem of defining a Hermitian phase operator. We discuss the limit of validity of the standard, non-rigorous Mathieu equation, due to the onset of a higher order $\cos 2 \phi$ term in the Josephson potential, and also to the overcompleteness of the representation (the phase $\phi$ being the relative phase between the two condensates). We thereby unify the Boson Hubbard and Quantum Phase models. 
J. R. Anglin (1), P. Drummond (2), and A. Smerzi (3) ((1)Institute for   Theoretical Atomic and Molecular Physics, Harvard-S...