物理580

Quantum Mechanics I

2017/2018学年

2017年秋季学期/中心>

Instructor: Professor Eduardo Fradkin

物理系
伊利诺伊大学Urbana-Champaign
2119室ESB，MC-704，
1110 W Green St, Urbana, IL 61801-3080
Phone: 217-333-4409
传真：217-244-7704
E-mailefradkin@illinois.edu
http://eduardo.www.chinawangyintong.com/homepage/

Time: 2:00-3:20 pm Mondays/Wednesdays
地点：RM。144 Loomis
CRN:30709
信用：1 unit.
办公时间：星期二4:00 pm -5：00 PM，RM 2119 ESB

ta：Simon Lin
电子邮件：shanlin3@illinois.edu
Office Hours: Fridays 3-4 pm, Loomis Interaction Room (2nd floor, LLP)

ta：min li
电子邮件：minl2@illinois.edu
Office Hours: Thursdays 2-3 pm, Loomis Interaction Room (2nd floor, LLP)

物理系提供了两学期的研究生水平量子力学，物理学580和物理学581。这两个课程本质上都被认为是一门课程，物理580涵盖了基本材料和物理581 581更高级的主题。在2017/2018年春季学期，将教授高级量子力学研究生量子力学水平，物理学581。对于物理580，我会假设学生在此处提供的本科课程的水平上熟悉量子力学。我还将假设学生们熟悉古典力学的拉格朗日和哈密顿的描述，例如兰道和菲尔希兹和/或戈德斯坦的水平。我将假设学生熟悉复杂变量功能的线性代数，向量空间和微积分的基本概念，尤其是对轮廓集成和残基的方法，以及部分差分方程中的标准材料。在这里提供的MMA和MMB课程中所涵盖的许多必要背景。敦促学生在上课之前审查此背景材料。我准备了有关此材料的一组笔记。在下面，您将找到指向这些笔记的链接。

公告

课程计划

数学背景

Review of the mathematics underlying Quantum Mechanics. Linear vector spaces. Inner product. Dual spaces. Dirac notation. Subspaces. Linear operators. Linear transformations. Hermitean and self-adjoint operators. Eigenvalues and eigenvectors. Finite dimensional and infinite dimensional spaces. This is a review of material that you should know from your undergraduate math classes.

古典力学的评论

The Lagrangian and the Action. The Least Action Principle. Hamiltonian formulation of Classical Mechanics. Poisson brackets. Relation between symmetries and conservation laws in Classical Mechanics.

The Postulates of Quantum Mechanics

古典力学有什么问题？黑体辐射和普朗克光谱。光电效果。原子光谱。双缝实验。颗粒和波。光子极化实验。

量子状态。测量和波函数。操作员和物理可观察物。不确定性原则。叠加原则。对应原理和经典限制。量子力学的概率解释。能量和动力。汉密尔顿运营商。静止状态。 The Heisenberg representation of operators. The density matrix. Momentum. Uncertainty Relations.

Schrödinger方程第1部分第2部分第3部分

Schrödinger方程。特性。概率电流。静止状态。量子机械运动在一个维度上。潜力很好。线性谐波振荡器。统一场。传输系数。在磁场上运动在两个维度上。 The Aharonov-Bohm effect. The integer quantum Hall effect.

量子力学中的对称性

对称转换。转化组。点组。连续组和角动量理论。表示。不可证明的表示。角动量的特征值和特征向量。矩阵元素。平价。添加角动量。

Motion in a Central Field

Spherical waves. The hydrogen atom. Partial wave decomposition of a plane wave. Motion in a Coulomb field. Bound states and scattering states.

散射理论

经典和量子力学中的散射过程。绿色功能。交叉区域。时间无关的扰动。天生的近似值

扰动理论

时间独立的扰动。瑞利 - 雪人和布里鲁因束扩展。保护法的作用。退化状态。申请。

半古典限制

波函数和半古典限制。波数据包。Bohr-Sommerfeld量化规则。多变的kramers-brillouin近似。隧道。

Path Integrals and Quantum Mechanics

Path integrals and the Superposition Principle. The Feynman Path Integral. Path integrals in imaginary time and Statistical Mechanics. Calculus of path integrals for harmonic systems. Functional determinants. The semi-classical approximation. 双井和隧道.

Syllabus for量子力学II, Physics 581, Spring Semester 2018

Grades

There will be a total of七(7) homework sets. The last set will be your最终的exam. The final exam will weigh 1/7 of the grade and the homework sets the remaining 6/7. The homework sets are due on the due date posted on this webpage and have to be deposited at the TA's mailbox before midnight on that date. There will be a 20% grade penalty on late homework sets and no homework sets will be accepted of they are more than two days late (barring extenuating circumstances which will only be considered by the Instructor, not by the TA).

您可以通过查看您的入口来检查您的成绩物理580年级

作业

作业1号;PDF文件

发布于2017年7月30日，星期日；到期日：2017年9月20日，星期三，下午5:00

Solutions to Homework Set No. 1

作业2号;PDF文件

发布于2017年9月20日，星期三；到期日：2017年10月6日，星期五，下午5:00

Solutions to Homework Set No. 2

Homework set No. 3;PDF文件

posted Wednesday October 4, 2017;Due date:Friday October 20, 2017, 5:00 pm

Solutions to Homework Set No. 3

Homework set No. 4;PDF文件

发布于2017年10月20日，星期五；到期日：Friday November 3, 2017,编辑版本于10月30日发布

Solutions to Homework Set No. 4

Homework set No. 5 PDF文件

发布于2017年11月6日，星期一；到期日：Friday November 17, 2017

Solutions to Homework Set No. 5

Homework set No. 6;PDF文件

posted Friday November 17, 2017; Due date:2017年12月8日，星期五，下午5:00

Solutions to Homework Set No. 6

第7号作业/参加期末考试;PDF文件

发布于2017年12月9日，星期六；到期日：2017年12月17日，星期日，下午5:00

Note: This is a take-home Final Exam. The solutions must send me by email (to efradkin@illinois.edu) the pdf file with your solutions before Sunday 12/17/2017 at 5:0 0pm. You should not give the solutions to the TA nor put them in the Physics 580 homework box. No late sets will be accepted. Since this problem set is a take home Final Exam, you must turn in your solutions to pass this course. You must make sure that the pdf file is clearly legible!. Please either prepare the solutions in LaTeX . If your solutions are handwritten you must write them with dark pen with clearly legible handwriting in double spaced paper. I cannot grade solutions with bad handwriting and/or with random organization. They must be clearly organized with your results shown clearly.

参考书目

必需的教科书

R. Shankar, "Principles of Quantum Mechanics", Second Edition, Plenum Press (1994).

J. J. Sakurai, "Modern Quantum Mechanics", Revised Edition, Addison-Wesley Longman (1994).

推荐的教科书

L. D. Landau and E. M. Lifshitz, "Quantum Physics", Third Edition , Course of Theoretical Physics, Volume 3. Pergamon Press (1991).

Gordon Baym, "Lectures on Quantum Mechanics", Addison Wesley (1990).

Eugene Merzbacher，“量子力学”，第二版，J。Wiley＆Sons（1970）。

伦纳德·希夫（Leonard Schiff），《量子力学》，第三版，麦格劳 - 希尔（McGraw-Hill）（1968）。

Albert Messiah, "Quantum Mechanics", Dover (1999).

Paul A. M. Dirac，“量子力学原理”，牛津科学出版物，第四版（1958）。

Richard P. Feynman, Robert B. Leighton and Matthew Sands, "The Feynman Lectures on Physics", Volume 3, Addison Wesley (1969).