Then time-dependent invariant is introduced and a kind of method to solve the Schrodinger equation explicitly called Gauge transformation method.
稍后引入含时不变量的定义，以及精确求解薛定谔方程的含时规范变换方法，再次讨论了Aharonov-Bohm效应，Berry相位和绝热近似。
This part is arranged as follows: In chapter 1, we give a brief review of the progress of theory and experiment on single-molecule magnets, including Mn12, Fe8, Mn4 and supermolecular magnetic cluster [Mn4]2. In chapter 2, we introduce some basic theoretical descriptions about quantum resonant tunneling and some experimental results, taking example for Mn12 system. In chapter 3, we give a study of the staircase hysteresis loop of Mn12 system based on Landau-Zener model and numerically calculation method of exact diagonalization of Hamiltonian. In chapter 4, we study the quantum resonant tunneling in supermolecular magnetic cluster [Mn4]2 system by means of the numerically exact solution of the time-dependent Schrodinger equation.
第一部分共有五章：第一章，我们简要回顾了，关于单分子磁体Mn12、Fe8、Mn4和超分子磁团簇[Mn4]2在理论和实验上的发展过程；第二章，我们以Mn12体系为例，介绍了关于量子共振隧穿的一些基本理论描述，以及一些实验结果；第三章，我们给出了用Landau-Zenner模型和严格对角化的数值计算方法，对Mn12体系中阶梯状磁滞回路所作的一些研究；第四章，我们用数值求解含时薛定谔方程的方法，研究超分子磁团簇[Mn4]2体系的量子共振隧穿过程；第五章，我们提出一种唯象的局域热平衡方法，研究Mn12体系热助隧穿的动力学过程。
In this thesis, we propose a fully discrete scheme by using the artificial boundary technique for one-dimensional time-dependent Schrodinger equation on unbounded domain, and give its theoretical analysis.
本文对一类一维无界域上依赖于时间的薛定谔方程，构造了一种基于人工边界方法的全离散有限元格式，并对其作理论分析。
The ionization probability and high-order harmonic spectrum of hydrogen atom under different laser pulse are computed by solving the time-dependent Schrodinger equation of hydrogen atom in a intense laser field, in which an algorithm of split-operator is quoted.
采用二阶劈裂算子算法，通过数值求解强激光场中基态氢原子的含时薛定谔方程，计算了不同的激光脉宽下氢原子的电离率和高次谐波。
The single atom emission spectrum was obtained by solving numerically the time-dependent Schrodinger equation of two-level atom under strong laser field.
通过数值求解强激光场作用下两能级原子的含时间薛定愕方程得到了单原子辐射谱，并与解析解得到的单原子谐波谱进行了比较。
Considering the time-dependent generator coordinate method, the time-dependent Schrodinger equation for nuclear collective motions is obtained.
考虑依赖于时间的生成坐标方法，给出了依赖于时间的集体运动的薛定谔方程。
In the study of 1D quantum nonlinear lattices, especially in the study of dynamics, it is unavoidable to solve the many-body time-dependent Schrodinger equation.
在一维量子非线性晶格的研究中，特别是动力学的研究中，求解多粒子体系的含时薛定谔方程是不可避免的。
The time-dependent Schrodinger equation of realistic hydrogen atom in intense laser field and static electric field is solved by split-operator method, and the abnormal behaviors of high-order harmonic generation (HHG) in intense laser field is investigated, which is caused by a static electric field.
利用分裂算符方法数值求解了真实氢原子在强激光场和静电场作用下的含时薛定谔方程，研究了静电场对强激光场中氢原子产生高次谐波的影响。
The general time-dependent SchrOdinger equation with external perturbance needs to be resolved through Lie group decompositions.
而一般具有外加微扰作用力的含时薛定谔方程的求解需要通过李群分解。
By solving the time-dependent Schrodinger equation with a one-dimensional short range potential, the effect of initial population on the high harmonics generation was studied.
通过数值求解一维短程势含时薛定谔方程，研究了初始粒子数布居对谐波辐射的影响。
In chapter 4, we study the quantum resonant tunneling in supermolecular magnetic cluster [Mn_4] _2system by means of the numerically exact solution of the time-dependent Schrodinger equation.
第四章，我们用数值求解含时薛定谔方程的方法，研究超分子磁团簇[Mn4]2体系的量子共振隧穿过程；
We performed extensive computer simulations on the CEPD effect on photoionization of hydrogen atom by numerically solving the time-dependent Schrodinger equation.
我们对一维模型氢原子光电离的CEPD效应进行了数值模拟的计算机实验，通过对含时薛定谔方程的数值求解，得到氢原子光电离的一些合理结论。
Quantum trajectories were calculated through wave function by a numerical solution of the time-dependent Schrodinger equation. The probability density functions and quan-tum trajectories representing electron diffraction in real space were obtained from the calculation.
通过数值求解含时薛定谔方程计算波函数，然后计算电子运动的量子轨迹，由此得到表征电子衍射行为的实空间几率密度函数和量子轨迹。
The standard method solving the time-dependent Schrodinger equation is seriously restricted, by which the computational efforts scale exponentially with the number of degrees of freedom.
求解含时薛定谔方程的标准方法由于其计算量与体系的自由度呈指数增长而大受限制。众所周知，标准的方法只适用于不超过五、六个自由度的体系。
We solve time-dependent Schrodinger equation of one-dimensional atom in intense laser field with pseudospectral method by introducing nonlinear space transformation.
本文通过引入非线性空间变换，用伪谱方法数值求解了一维原子在强激光场中的含时Schr（？）