【摘要】 讨论哈密顿不依赖于时间的系统的非绝热几何位相，结果证明：对于这样的系统，除了定态是几何位相为零的循环态之外，循环态条件仅在如下情况满足：①两能级系统或只有两个本征态的几率幅不为０；②系统的激发能是可公度的．如果循环态存在，系统的非绝热几何位相与初态｜ψ（０）＞有关更多还原

【Abstract】 Non adiabatic geometrical phase of a system with time independent Hamiltonian is discussed. The results show that apart from the stationary state, which is the cyclic state without geometrical phase, the condition of cyclic state can be satisfied in the following cases:only two eigenstates have non zero probability amplitudes in the state, the exitation energies are commensurate. The results also show that the cyclic state, the non adialatic geometrical phase and the dynamical phase depend on the initial state.更多还原