| 课程号 |
00432206 |
学分 |
2 |
| 英文名称 |
Advanced topics in Quantum Mechanics |
| 先修课程 |
量子力学 |
| 中文简介 |
目前，国内现有的量子力学课程着重讲授非相对论性量子力学的基本理论和方法，对其路径积分形式的表述和实际具体的计算方法、解决具体实际问题的应用等大多不予深入讨论、甚至根本不提及，对于从量子力学到量子场论的过渡大多也不予讨论。该专题课程针对解决这些问题而开设，从而帮助同学打下从量子力学的形式理论过渡到开展具体物理研究的坚实基础。
本课程主要讲授非相对论性量子力学在描述一些基本量子现象的应用（比如能谱、量子动力学、散射理论、隧穿理论、AB效应和Berry相位等）和量子力学中的路径积分、格林函数及其它一些基本问题的实际计算方法（比如半经典近似、变分法、数值计算方法、一些精确可解模型、 微挠的费曼图展开理论等等）。课程将采用新的理论框架（路径积分和其相关计算技术）来描述量子现象，从而为同学们进一步学习量子多体理论等后续课程打下扎实的理论基础。该课程将在突出清晰的物理概念的同时，强调具体计算技能（包含解析和数值两方面），并结合当前的研究实例来展开。 |
| 英文简介 |
The course provides a deeper understanding of general phenomena in systems that behave essentially quantum mechanically and practical introductions to methods used to describe the behavior.
The phenomena discussed include the nature of spectrum, quantum dynamics, scattering and tunneling. In addition to a survey of exactly solvable problems, a variety of approximations are introduced: from perturbation theory, semiclassical, variational to numerical simulation. General tools of the Green’s functions and path integrals are also introduced and utilized. |
| 开课院系 |
物理学院 |
| 通选课领域 |
|
| 是否属于艺术与美育 |
否 |
| 平台课性质 |
|
| 平台课类型 |
|
| 授课语言 |
英文 |
| 教材 |
Modern Quantum Mechanics,Sakurai,Addison Wesley,2010；
Essential Quantum Mechanics,Bowman,Oxford University Press,2008；
Quantum Mechanics and Path Integrals,Feynman et.al.,Dover Publications,2010；
Introduction to Quantum Mechanics,Griffiths,Benjamin Cummings,2004；
Quantum Mechanics,Claude Cohen –Tannoudji et.al.,Wiley-Interscience,2006；
Quantum Mechanics： An Introduction,Greiner,Springer,2008；
“Quantum Mechanics”,A. Konishi and G. Paffuti,Oxford University Press, London.,2009；
“Green’s Functions in Quantum Physics”,E.N. Economou,Springer-Verlag, New York,2006；
Quantum Mechanics. Symmetries,Greiner,Springer,2008；
Quantum Mechanics Non-Relativistic Theory,Landau, Lifshitz,Butterworth-Heinemann;,1981；
Principles of Quantum Mechanics,R. Shankar,Springer,1994；
Schaum`s Outline of Quantum Mechanics,Yoav Peleg et.al.,McGraw-Hill,2010；
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| 参考书 |
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| 教学大纲 |
课程将采用新的理论框架（路径积分和其相关计算技术）来描述量子现象，从而为同学们进一步学习量子多体理论等后续课程打下扎实的理论基础。该课程将在突出清晰的物理概念的同时，强调具体计算技能（包含解析和数值两方面），并结合当前的研究实例来展开。
I. Review of Quantum Mechanics via Solvable Models
A. Another look at elementary one particle quantum mechanics
(1) Spectra of the single particle Schroedinger equation: discrete versus continuous.
(2) Extreme quantum limit: completely discretized spectrum.
(3) The opposite extreme: purely continuous.
(4) Mixed spectrum.
(5) Methods to tackle a QM problem.
B. Solvable linear and SUSY Models. Bosonic degree of freedom
(1) Harmonic oscillator solved using the (boson) creation and the annihilation operators.
(2) Coherent states and field quantization. Harmonic oscillator as a paradigm of bosonic degree of freedom.
(3) Generalization to general supersymmetric potential.
(4) Landau – Bronshtein quantization in magnetic field.
C. Other solvable Models. Two level system as a fermionic degree of freedom
(1) Another method: matching solvable models at boundaries.
(2) Bound states in a well.
(3) More wells. Hilbert space truncation and the paradigmic fermionic degree of freedom.
(4) Integral transformation for the delta function potentials.
II. Numerical method of the solutions of QM problems.
(1) Discretization of a continuous variable.
(2) Simulation of Time Dependent Schroedinger Equation (TDSE).
III. Major tools: Green’s functions and path integral
A. Global and local density of states (DOS).
B. Green’s functions (GF)
C. The path (functional) integral representation of GF
IV. Perturbation theory and Green’s functions
A. Time independent perturbation theory
B. Scattering and time independent perturbation theory
C. Diagrammatic perturbation theory
V. Semiclassical and variational methods
A. Semiclassical methods
B. Semiclassical methods via path integral
C*. Adiabatic evolution in semiclassical approximation
D. Gaussian variational approach
多媒体.强调互动，课堂上希望同学能带笔记本，并用mathematica软件即时计算
平时成绩40%，笔试 60%
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| 教学评估 |
B. Rosenstein：
学年度学期：16-17-3，课程班：量子力学专题1，课程推荐得分：3.75，教师推荐得分：3.75，课程得分分数段：80及以下；
学年度学期：17-18-3，课程班：量子力学专题1，课程推荐得分：3.75，教师推荐得分：3.33，课程得分分数段：80-85；
学年度学期：18-19-3，课程班：量子力学专题1，课程推荐得分：0.0，教师推荐得分：7.5，课程得分分数段：80-85；
学年度学期：22-23-3，课程班：量子力学专题1，课程推荐得分：null，教师推荐得分：null，课程得分分数段：80及以下；
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