课程大纲

COURSE SYLLABUS

课程代码/名称

Course Code/Title

PHY5033 高等量子力学 B Advanced Quantum Mechanics B

课程性质

Compulsory/Elective

专业核心课

课程学分/学时

Course Credit/Hours

3/48

授课语言

Teaching Language

英文/English

授课教师

Instructor(s)

李贵新教授

是否面向本科生开放

Open to undergraduates

or not

否

先修要求

Pre-requisites

General Physics

教学目标

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.

教学方法

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.

教学内容

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,

Fermi’s 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.

课程考核

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