【作者】 钟任斌；

【导师】 黄整；

【作者基本信息】 西南交通大学 ， 光学工程， 2003， 硕士

【摘要】 时域有限差分(FDTD)法是在时域中求解电磁场的一种数值计算方法。它把带时间变量的Maxwell微分方程转化为差分方程来求解其电磁场各分量。自从FDTD法创建以来，它主要被应用于研究一般的电磁场和电磁波计算，而用于量子力学计算研究的报导还较少见。 本文首先简要介绍了FDTD法的基本理论和发展，以及一般量子力学计算的常用方法，分析了双原子分子势能函数形式和双原子分子光谱特点。重点阐述了FDTD法应用于双原子分子光谱量子力学的计算，并在对边界作近似截断处理条件下计算了氧分子的基态和激发态的振动光谱。 其次，考虑到其应用范围的推广、物理模型的合理性以及数学逻辑上的严密性，本文以能量守恒为基础对前人提出的近似边界截断处理方法进行了改进，使得FDTD法应用于双原子分子光谱的量子力学计算在理论上更为合理，并将改进后的方法应用于氮分子的基态和激发态振动光谱计算。 最后，将计算所得光谱常数与实验结果进行了分析对比，结果令人满意。表明FDTD法本身及其改进后的截断处理在双原子分子振动光谱的量子力学计算方面是可行的。 FDTD法用于双原子分子量子力学计算不需要使用完备的基函数集合构造波函数，从而避免了因为基函数数目的无限大与实际计算的有限性之间的矛盾。该方法可直接用于时域计算、适于编写通用程序和并行计算，具有简单、直观、易于掌握的特点，从而为量子力学计算在方法上提供了一种新的选择。更多还原

【Abstract】 Finite-difference time-domain method is a numerical calculation method of finding the solution to the electromagnetic field in the time-domain. It transfers Maxwell Differential Equation with time variant to difference equation so as to find the solution to the electromagnetic field. Since the foundation of FDTD method, it is mainly used in the calculation of the electromagnetic fields and waves. However, there are few reports of the application in the calculation of quantum mechanics.Firstly, the theories and development of the FDTD method were briefly introduced and the traditi6nal method of quantum calculation was offered. The potential energy functions and the spectrums’ characteristic of diatomics were analyzed. The application of FDTD method in vibrational spectrums for diatomics was expatiated, and the vibrational spectrums of ground and excited states for oxygen molecule were calculated with this method by the approximate boundary cut-off .Secondly, considering rationality of physical model and the strictness of mathematical logic, a novel method to cut-off the boundary was suggested based on the conversation of energy, which makes FDTD more reasonable in the application for the quantum calculation of diatomics spectrums. The improved boundary cut-off method is applied in the calculation of the vibrational spectrums for the ground and excited states of oxygen.Finally, the spectrum constants were compared with the experimental data and the results are acceptable. Thus it is indicated that FDTD method and the novel boundary cut-off is feasible on the calculating for the vibrational spectrums of diatomics.FDTD method doesn’t need a complete basic set of functions to construct the wave function, therefore the contradiction between the infinity of the number of basic functions and the finity of practical calculation is avoided. FDTD method is feasible for the direct time-domain calculation, the development ofcommon program and parallel calculation. The method is simple, convenient and easy to be master, and is a new choice for the quantum calculation.更多还原