中文摘要：

综述量子力学相位问题的背景、产生及进展。最初由Berry提出的适用于线性系统绝热演化的Berry相位受到了局限,在实际应用中,Berry相位被推广到非绝热演化（AA相）、非循环过程（非对角几何相）及非线性系统（一般量子态的几何相位）。指出对于非线性系统非对角几何相的研究是个新的研究课题,并对其研究前景进行展望。

英文摘要：

The background and evolvement of phase problem in quantum mechanics is overviewed. Berry phase which was brought up originally by Berry M.V. for adiabatic evolution in linear systems is limited in practical applications. Berry phase is generalized to nonadiabatic evolution （AA phase）, noncyclie quantum evolution（ off-diagonal geometric phase）and nonlinear systems（ geometric phase of general quantum states）. It is pointed out that the off-diagonal geometric phase in nonlinear system is a new area for research. The prospect of this subject is viewed as well.