关键词: 量子力学, 含时微扰论, 相因子

Abstract: Textbooks on quantum mechanics usually assert that perturbation theory holds true only for sufficient short time. This mistake results from direct contribution of the non-periodical time term into probabilities. We first introduce a fundamental theorem in the time-dependent quantum theory，then point out that the non-periodical time terms are in fact perturbation expansions of time-dependent phase factor.

Key words: quantum mechanics, time-dependent quantum theory, phase factor