On the Bosonic Phase Operator Realization for Josephson Hamiltonian Model

On the assumption that a Cooper pair acts as a Bose particle and based on the newly established <η|representation, which is the common eigenvector of two particles' relative position and total momentum, we introduce a mesoscopic Josephson junction Hamiltonian constituted by two-mode Bose phase operator and number-difference operator. The number-difference-phase uncertainty relation can then be set up, which implies the existence of Josephson current.