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对于可参数化时间t的周期Hamiltonian系统，由non－adiabatic到adiabatic－limit的“严格”演变以获得Berry几何相γn（C）的问题．结果表明，存在“四种类型”的演变态，它们都可以满足在参数R空间中的同一条闭合曲线C上作这样的“严格演变”，并且还都可以获得同一个Berry几何相γn（C）；而Berry发现这一几何相γn（C）时所考虑和采用的“演变态”，恰好属于本文“四种类型”的“严格”演变态之一的adiabaticapproximation情形．据此，可以把Berry几何位相理论推广到本文所研究的“四种类型”的“严格”演变中．
For a periodic Hamiltonian system that can parameterize time t, the “rigorous” evolution from non-adiabatic to adiabatic-limit to the Berry geometry phase γn (C) problem. The results show that there are “four types” of evolution states that all satisfy the “rigorous evolution” of the same closed curve C in the parameter R space and also obtain the same Berry geometry phase γn (C ); And the “evolutionary state” considered and adopted by Berry when he discovered this geometric phase γn (C) happens to belong to the adiabaticapproximation case, one of the “rigorous” evolutionary states of the “four types” of this article. Accordingly, Berry’s geometric phase theory can be generalized to the “rigorous” evolution of the “four types” studied in this paper.