课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
PHY5033 高等量子力学 B Advanced Quantum Mechanics B
2.
课程性质
Compulsory/Elective
专业核心课
3.
课程学分/学时
Course Credit/Hours
3/48
4.
授课语
Teaching Language
英文/English
5.
授课教
Instructor(s)
李贵新教授
6.
是否面向本科生开放
Open to undergraduates
or not
7.
先修要
Pre-requisites
General Physics
8.
教学目
Course Objectives
Quantum mechanics are essential to materials science and engineering at the atomic, molecular and
crystal scales. Important optical, electrical, and magnetic properties of materials can only be well
understood within the realm of quantum mechanics. This course is an introductory course for quantum
mechanics with emphasis on applications in materials science. The objective is to provide students in
materials science and engineering with basic concepts in quantum mechanics and apply the principles and
methodologies to understand materials properties and device applications. Topics to be covered include
Shrodinger s wave equation, Dirac notations, propagation in periodic potentials, quantum harmonic
oscillators, and perturbation theory. By applying those quantum mechanical concepts, important
materials properties and phenomena including crystal structures, electron propagation in crystals,
molecular and lattice vibrations, and optical transitions are explained in detail. In addition,
operation principles for semiconductor lasers and resonant tunnelling devices are discussed using
quantum mechanical tools. After completing this course, students will have in-depth understanding of
important materials properties and build a solid foundation to explore frontier materials research.
9.
教学方
Teaching Methods
The course combines online lectures and classroom discussions for effective learning. Pre-recorded
lecture videos will be placed online for students to study before the classroom discussions. The same
lecture videos are available for students to review for multiple times to master the course materials.
During classroom lectures, core concepts will be recapitulated to help students learn the topics. The
knowledge points will be further clarified by answering and discussing student questions. To help
establish the ability of applying the knowledge, numerous examples regarding to important material and
device applications are illustrated by applying the concepts and theories of quantum mechanics. This
flipped classroom approach is believed to help students develop an in-depth understanding of the
course content.
A final group project will provide another opportunity to the students to develop knowledge mining and
knowledge application skills to address a current research topic related to quantum mechanics. The
group project will also help students collaborate and work in a team environment. The term paper and
project presentation will help students develop and hone their written and oral communication skills.
This course is taught in English, including lectures, discussions, homework, exams, term papers and
presentations.
10.
教学内
Course Contents
Section 1
Review of classical mechanics 1D harmonic oscillator, diatomic molecule,
monatomic and diatomic linear chains;
Section 2
Review of classical electromagnetism electrostatics and electrodynamics;
Section 3
Toward quantum mechanics Schrodinger wave equation, wave packet and
dispersion, hydrogen atom, crystal structure, electronic structures of bulk
semiconductors and heterostructures;
Section 4
Using the Schrödinger wave equation normalization and completeness,
currents due to tunnelling and traveling wave, symmetry and degeneracy
Section 5
Using the Schrödinger wave equation particle in a box, transmission,
reflection and tunnelling, nonequilibrium electron transistor;
Section 6
Electron propagation propagation matrix, time-reversal symmetry, current
conservation, rectangular potential barrier, resonant tunnelling;
Section 7
Electron propagation in a periodic potential the Block s theorem, tight
binding approximation, crystal momentum, effective mass, energy bands, the
WKB approximation
Section 8
Eigenstates and operators Dirac notation, the no cloning theorem, density
of states;
Section 9
The harmonic oscillator creation and annihilation operators, harmonic
oscillator wave functions, time dependence
Section 10
The harmonic oscillator quantization of electromagnetic fields, lattice
vibrations and mechanical vibrations
Section 11
Fermions and bosons Fermi-Dirac distribution and chemical potential,
Bose-Einstein distribution function
Section 12
Time-dependent perturbation first-order time-dependent perturbation,
Fermis golden rule, elastic scattering, photon emission
Section 13
The semiconductor laser absorption, spontaneous and stimulated
emissions, optical transition rules, gain in media, optical cavity
Section 14
The semiconductor laser laser diode rate equations, numerical solution to
rate equations, noise in laser diode emission
Section 15
Time-independent perturbation time-independent nondegenerate and
degenerate perturbations
Section 16
Angular momentum and the hydrogen atom angular momentum operator,
geometrical representation, spherical coordinates and spherical harmonics,
rigid rotator
Section 17
Final exam
11.
课程考
Course Assessment
Quiz: 5%
Homework: 20%
Midterm: 25%
Final exam: 35%
Project and presentation: 15%
12.
教材及其它参考资料
Textbook and Supplementary Readings
Textbook:
Applied Quantum Mechanics, Author: A. F. J. Levi, Publisher: Cambridge University Press 2nd ed. 2012,
ISBN: 0521183995
References:
Quantum mechanics : concepts and applications, Author: Nouredine Zettili., Publisher: Wiley 2nd ed. 2009,
ISBN: 9780470026793