|
所在平台: Coursera |
课程主页: https://www.coursera.org/learn/approximation-methods
课程评论：没有评论
课程名称：近似方法 课程概述：本课程也可以作为学分课程ECEA 5612，作为科罗拉多大学博尔德分校电气工程硕士学位的一部分。该课程教授量子力学中常用的近似方法，包括时间独立微扰理论、时间依赖微扰理论、紧束缚方法、变分法以及有限基集的使用。每种方法都将通过特定示例清晰展示其工作原理。 学习目标： 1. 使用时间依赖微扰理论获得能量和波函数的一阶和二阶修正； 2. 使用时间依赖微扰理论获得跃迁率； 3. 使用紧束缚方法、变分法和有限基集获得各种量子力学问题的近似解。 课程大纲： 第一部分：时间独立微扰理论 描述：在本模块中，我们将介绍量子力学中常用的近似方法，然后讨论时间独立微扰理论。我们将首先讨论非简并微扰理论，并导出一阶和二阶修正的有用公式。接着，我们将讨论简并微扰理论，并介绍各种微扰方法的实际应用示例，如斯塔克效应、精细结构和泽曼效应。 第二部分：时间依赖微扰理论 描述：在本模块中，我们将介绍相互作用图景并导出时间演化方程。在讨论一个简单但具启发性的两态系统示例后，我们将发展时间依赖微扰理论，并讨论由外部微扰引起的量子态之间的跃迁概率。 第三部分：其他近似方法 描述：本模块涵盖几种非微扰近似方法，包括紧束缚方法、变分法和有限基集的使用。 通过本课程的学习，学员将掌握量子力学中的多种近似方法并能够有效应用于相关问题的求解。
Part: 1
Title:Time-independent Perturbation Theory
Description:In this module we will introduce the course on approximation methods commonly used in quantum mechanics and then discuss time-independent perturbation theory. We will first discuss non-degenerate perturbation theory and derive useful formulas for the first- and second-order corrections. We will then discuss degenerate perturbation theory. We will also discuss specific examples where the various perturbation methods are used - Stark effect, fine structure and Zeeman effect.
Part: 2
Title:Time-dependent Perturbation Theory
Description:In this module, we will introduce interaction picture and derive time evolution equations. After discussing a simple but illuminating example of two-state system, we develop time-dependent perturbation theory and discuss the probability of transitions between quantum states induced by external perturbation.
Part: 3
Title:Other Approximation Methods
Description:This module covers several non-perturbative approximation methods. They are the tight binding method, variational method and the use of finite basis set.
This course can also be taken for academic credit as ECEA 5612, part of CU Boulder’s Master of Science in Electrical Engineering degree. This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational method and the use of finite basis set. In each case, a specific example is given to clearly show how the method works. At the end of this course learners will be able to: 1. use time-dependent perturbation theory to obtain first- and second -order corrections to energies and wavefunctions, 2. use time-dependent perturbation theory and obtain transition rates, and 3. use tight binding method, variational method and finite basis set to obtain approximate solutions of various quantum mechanics problems.
