Course Name: Quantum Mechanics
Lecture Time: 40 sessions, 2 hours/session
1. Property and Mission of the Course
Quantum mechanics is the basic theory about the law of movement of the material world and the foundations and pillars of modern physics. In the past 100 years, it has been tested by a large number of accurate experiments, has explained a wide range of natural phenomena, and has achieved unprecedented successes. It has not only penetrated into every field of physics, but also been widely used in many areas such as chemistry, life science, computer science.
Quantum mechanics is an important professional basic course for students in the physics department, but also provides indispensable basic knowledge and training of physical workers in modern physics research. Through the study of this special course, we hope students can master the basic principles of quantum mechanics and the basic methods to solve problems with quantum mechanics.
2. Teaching Goal of the Course
2.1 Obtain preliminary thoughts of quantization, and master five fundamental principles of quantum mechanics;
2..2 Use Schrodinger equation to solve the problem of the simple micro system, and master basic approximation methods of quantum mechanics for dealing with problems;
2.3 Allow students to understand the particularity of the contradiction of the microscopic world and the law of movement of microscopic particles, and preliminary mastery of principles and basic methods of quantum mechanics to lay the necessary foundation for further learning and research.
Topics and Schedule
1.1 Get to know research object, application scope of quantum mechanics, development of quantum mechanics, Bohr's quantum theory, wave-particle duality of light and particle;
1.2 Learn about the problems unresolved in classical physics, and the establishment process of quantum mechanics.
2. Wave Function and Schrodinger Equation
2.1 Correctly understanding essence of wave-particle duality and statistical interpretation of wave function1, understanding Schrodinger's building process, understanding the principle of superposition;
2.2 Master several typical solving methods of one dimensional steady state problem (One dimensional infinite potential well, One dimensional linear harmonic oscillator);
2.3 Understanding the statistical interpretation of the wave function and establishing process of Schrodinger equation, using the stationary Schrodinger equation to treat the potential well problem and linear harmonic oscillator problem.
3. Mechanical Quantity in Quantum Mechanics
3.1 Grasp the properties of the mechanical quantity operator, eigen value and eigen function of operator, properties of eigen function of the operator, eigen functions of common operators;
3.2 Comprehend commutation relationship of operators, energy level and wave function of hydrogen atom, change of operator with time;
3.3 Grasp the properties of the mechanical quantity operator, eigen function of the mechanical quantity operator, common operators and their eigen function, relationship between operator and mechanical quantity, commutation relationship of operators, uncertainty relation, conserved quantity.
4. Representation of State and Mechanical Quantity
4.1 Preliminary understanding of the concept of representation, and master the expression of state and mechanical quantity in special representation;
4.2 Master the expressions of relations in quantum mechanics in special representation, transformation between different representations, Dirac notation, and occupation number representation;
4.3 Master the expressions of states and mechanic quantities of quantum mechanics in special representation.
5. Perturbation Theory
5.1 Understand the commonly used approximation methods in quantum mechanics: perturbation theory and variational method; Introduce how to deal with the problem of non-degenerate stationary perturbation, degenerate stationary perturbation and time dependent perturbation by using the perturbation theory; Finally, discuss the absorption and emission of light;
5.2 Master perturbation theory and variational method, non-degenerate stationary perturbation, degenerate stationary perturbation and time dependent perturbation.
6.1 Understand and deal with two basic methods of scattering problem;
6.2 Master variational method and Born approximation.
7. Spin and Identical Particle
7.1 Understand spin properties, spin operator and spin function, coupling of angular momentum, Zeeman effect and fine structure, property and wave function of identical particle;
7.2 Master some methods for explaining some experimental phenomena using quantum mechanics.
Remark on Teaching
Through homework we will get to know the understanding conditionstudents’ level of understanding of the lectured content at any time and the homework grades will be included in the final total score. We will also assign some small research topics to extend classroom knowledge and to foster the ability to solve real physical problems by using quantum mechanics and the grades will be added to the final score Finally, by the final closed-book written examination we will investigate students’ comprehending and mastery situation of the basic content of this course.
Shi-Xun Zhou, a Course of Quantum Mechanics (the Second Edition),Higher Education Press, 2009
 Jin-Yan Zeng, Quantum Mechanics Vol Ⅰ, Ⅱ, the Fifth Edition, Science Publishing Company, 2013;
 Bo-Chu Qian, Quantum Mechanics, Higher Education Press, 2006;
 Jin-Yan Zeng, a Course of Quantum Mechanics, the Second Edition, Science Publishing Company, 2014;
 Bo-Chu Qian, Exercises Selection and Analysis of Quantum Mechanics, the Third Edition, Science Publishing Company, 2008;
 Ru-Keng Su, Quantum Mechanics, the Second Edition, Higher Education Press, 2002;
 David J. Griffiths, Yu Jia (Translator), Xing Hu (Translator), Yu-Xiao Li (Translator), Introduction to Quantum Mechanics, China Machine Press, 2009;
 W. Greiner [Germany], Quantum Mechanics: Symmetries, Peking University press, 2001;
 R. Shankar, Principles of Quantum Mechanics, the Second Edition, World Book Inc, 2007;
 ClaudeCohen-Tannoudji, BernardDiu, FranckLaloe, Jia-Mo Liu (Translator), Xing-Kui Chen (Translator), Quantum Mechanics Vol I, Higher Education Press, 2014;
 ClaudeCohen-Tannoudji, BernardDiu, FranckLaloe, Jia-Mo Liu (Translator), Xing-Kui Chen (Translator), Quantum Mechanics Vol II, Higher Education Press, 2016;
 J. J.Sakurai，Jim Napolitano， Modern Quantum Mechanics, the Second Edition, World Book Inc, 2011.