GEOMETRIC PHASES AND SCHR?DINGER'S CAT STATE

A matrix method is presented for treating the dynamical phases, adiabatic phases and nonadiabatic phases of quantum superposition states. It is effective for any parameter-varying Hamiltonian system. As two examples, the evolution of mass-varying harmonic oscillator and the evolution of coherent states under parameter-varying displaced operator have been studied, Some new phenomena are obtained in the first case and the possible producing of so-called Schr\ddot\rm odinger's cat state by geometric phases is pointed out. The quantum state useful for the quantum optical verification of Berry's phase is introduced.