【作者】 李凯；

【导师】 田贵花；

【作者基本信息】 北京邮电大学 ， 理论物理， 2010， 硕士

【摘要】 本篇论文主要包括两方面内容。第一部分是对广义椭球函数在权重s=2和s=-2的情况下能量本征值和本征函数的推导；第二部分讨论随机引力理论中的一个重要的概念-主方程,在Drude谱情况下的系数的形式。全文共分为三章：第一章是综述。简要介绍广义椭球函数和主方程的基本概念,研究意义,以及广义椭球函数和主方程的研究现状。其中包含广义椭球波动方程的形式,应用领域等；随机引力理论相关知识,以及主方程的研究意义及其研究现状。第二章我们将利用超对称量子力学方法试探性的推导出权重s=2和s=-2时广义椭球函数的形式。首先,我们使用超对称量子力学方法近似的计算出前几阶超势和广义椭球函数的本征值；接着根据之前所求得的超势和本征值推导出广义椭球函数一阶基态波函数。最后,利用势能的形不变特性,使基态波函数与激发态波函数建立一种递推关系,从而给出激发态波函数的解。该超对称量子力学方法的引入及一阶基态波函数形式将有利于广义椭球函数深入研究。第三章我们将在低温近似的情况下,利用拉普拉斯变换法来求解Drude谱主方程的的系数。首先我们将使用拉普拉斯变换求解Drude谱主方程系数满足的初等函数ui(i=1,2)；接着通过这两个初等函数求出关于它们的格林函数Gi(i=1,2)；同时根据Drude谱推导出噪声核；最后推导出Drude谱主方程的系数。这些系数将有利于进一步求解主方程。更多还原

【Abstract】 There are two parts in this thesis. The first one is derivation about the eigenvalues and the eigenfunctions of the spheroidal functions in the case of s=2 and s=-2. The second one is for deriving the coefficients of master equation, given the Drude special density, which is one of the important concepts in stochastic gravity theory. They are described in three chapters as following:In Chapter 1, the base concepts, research significance and the situation of Spin-weighted Spheroidal wave function and the master equation are introduced, including the formation of the Spin-weighted Spheroidal wave function and the applications etc; At the same time, there is the related knowledge about stochastic gravity theory and the research significance and the present research of master equation.In Chapter 2, we will try to derive the formations of the spin-weighted spheroidal wave function in the case of s=2 and s=-2, using the method of super-symmetric quantum mechanics. First of all, we use this method to calculate super-potential and eigenvalues of spheroidal functions in the first several terms. Further more, we derive the ground eigenfunction in the first order terms. At last, we will utilize the properties of the shape invariant of the potential energy to build the recurrence relation between the ground state wave function and the wave functions of the excited states and obtain the solution of these wave functions of the excited states. This super-symmetric quantum mechanics method and the formation of the ground state wave function are very useful for applying of the spheroidal wave function probably. In Chapter 3, we will attempt to derive the coefficients of the master equation in the special case: Drude spectral density, via the Laplace transformation, at low-temperature approximation. First, we utilize the Laplace transformation method to solve the elementary functionsu,(i= 1,2), which could constructed the coefficients of Drude’s master equation, and then we try to calculate the Green functions Gi(i= 1,2), which are the compound functions of the elementary functions ui;(i= 1,2); At the same time, we could obtain the noise kernel according to Drude spectral density. At last, we will derive the coefficients of Drude’s master equation, which are propitious to solution of the master equation.更多还原