Firstly , decoupling theory is applied to analyze multiplicative colored noise in a single mode laser system . steady state intensity distribution function with colored noise is obtained . the first - order - like phase transition driven by multiplicative colored noise is studied and compared with the case of multiplicative white noise 首先用退耦理论分析了单模激光场中的乘性色噪声，导出了含有色噪声的激光场定态强度分布函数，讨论了乘性色噪声诱导一级相变的条件。
Two different kinds of approximate theories for analyzing colored noise are employed in the nonlinear system . then effects of the colored nature of the noise on the statistical properties of the laser system , the stochastic resonance of bistable system , and the steady - state probability current of quasi - periodic system are investigated 本文主要通过两种不同的色噪声近似理论，分析了非线性系统噪声的有色性对激光系统的统计性质、准周期性系统的定态几率流和双稳系统中的随机共振现象的影响。
In this paper , the current states of research about the basic theory of stationary state perturbation method are firstly reviewed , on base of them , and studied some physics issues mainly about hydrogen atom . the stark effect of the energy level ( n = 4 ) of hydrogen atom is calculated and the stark effect of three dimensional hydrogen atom is discussed by the use of the parabolic coordinates , then the perturbative matrix elements for each energy level are given 本文首先综述了关于定态微扰论基本理论的研究现状，在此基础上利用定态微扰论对某些物理问题，主要是对氢原子问题展开了研究，计算了氢原子n = 4能级的斯塔克效应，并利用抛物线坐标法求解了三维氢原子的斯塔克效应，给出了氢原子斯塔克效应中微扰矩阵元的普遍公式。
