Syllabus - UofL Department of Physics & Astronomy



Syllabus

Physics 556: Quantum Theory and Matter (Credit units: 3)

(Spring 2011)

Lecture Room: 104 Natural Sciences BLDG

Lecture Time: 11:00 am-11:50 pm (Monday, Wednesday, & Friday)

Textbook: Quantum Mechanics: Concepts and Applications

by N. Zettili (John Wiley & Sons) (Second Edition)

Reference book: (1) Introduction to Quantum Mechanics

by David J. Griffiths, second edition (Pearson Prentice Hall);

(2) Introductory Quantum Mechanics

by Richard L. Liboff (Holden-Day, Inc);

(3) Principles of Quantum Mechanics

by Ramanurti Shankar (Plenum Press);

(4) Quantum Mechanics: A New Introduction

by Kenichi Konishi & Giampiero Paffuti (Oxford University Press)

Instructor: Dr. Ming Yu

Office: Room 242, John W. Shumaker Research Building

Office Hour: 2:00 pm – 5:00 pm (MW)

Phone Number: 502-852-0931

E-mail: m0yu0001@gwise.louisville.edu

Web site:

Description: This course is the second part of the two-semester course of quantum mechanics (Phys 555 and Phys 556). This course (Phys 556) will cover the topics of Schrödinger equation and solutions in three-dimension problems, the addition of angular momenta, identical particles for systems with more than one particles, the methodology in application of quantum mechanics including the perturbation theory and the variational principle which will be used to study the fine structure of hydrogen atom, helium atom, atomic spectroscopy, as well as the scattering.

Goal

The goal of this course will continue to broaden and deepen our knowledge, to develop critical thinking skills, and to develop problem-solving skills. The key elements related to this goal will include: introducing the identical particles in quantum mechanics, dealing with the exact solutions of the Schrodinger equation in three-dimensional problems and the addition of angular momenta, introducing the approximation approaches to solve the Schrodinger equation for complex systems as well as time-dependent Schrodinger equation, discussing fine structure of hydrogen atom, helium atom, atomic spectroscopy, as well as the scattering theory. You are encouraged to read the chapters and sections related to the topics from the textbook and reference books and to discuss with your fellow students or the instructor to make clear in concepts and in solving assigned problems. Your progress in this area will be assessed with a graded assignment (homework assignment, quiz set, and embedded in exam questions, etc.).

Course Requirements: PHYS 300, 450, 460, and 555.

Topics covered

1. Three-Dimensional Problems (Chapter 6)

1. 3D Problems in Cartesian Coordinates

2. 3D Problems in Spherical Coordinates (Central Force Problems)

3. The Hydrogen Atom

2. Addition of Angular Momenta (Chapter 7)

1. Addition of Two Angular Momenta

2. Coupling of Orbital and Spin Angular Momenta

3. Scalar, Vector, and Tensor Operators (optional)

3. Identical Particles (Chapter 8)

1. Many-Particle Systems

2. Systems of Identical Particles

3. The Exclusion Principle and the Periodic Table

4. Quantum Statistical Mechanics (optional)

4. Time-Independent Perturbation Theory (Chapter 9.2)

1. Nondegenerate Perturbation

2. Degenerate Perturbation Theory

3. The Fine Structure of Hydrogen

4. The Zeeman Effect

5. The Variational Principle (Chapter 9.3)

1. Theory

2. The Ground State of Helium

3. The Hydrogen Molecule Ion

6. Time-Dependent Perturbation Theory (Chapter 10)

1. The Picture of Quantum Mechanics

2. Time-Dependent Perturbation Theory

3. Emission and Absorption of Radiation (Optional)

7. Scattering (Chapter 11)

1. Scattering and Cross Section

2. Scattering Amplitude of Spinless Particles

3. The Born Approximation

4. Partial Wave Analysis (optional)

5. Scattering of Identical Particles

Homework

Homework assignments will be distributed at beginning of each week. The Homework includes both general problems and challenge problems. You are asked to accomplish the general problems and encouraged to take the challenge problems. Your solutions for each problem must include not only the final answers but intermediate steps. The corresponding due dates for Homework will be written on the Homework assignments. Homework assignments will be collected and graded, and form part of your final score. You may discuss homework problems with your fellow students. In fact, you are encouraged to work as a group. However, the final write-up must be your own.

Quiz

There may be two conceptual quizzes. Some extra points will be given.

Exams

There will be a midterm exam and a final exam. The midterm exam is scheduled on March 11/23, and the final exam is scheduled on April 25/May 2. Each exam will have an “in-class” and a “take-home” section. They are weighted as one-third and two-third, respectively.

Class Participation

Class participation will be monitored throughout the semester. You are basically required to attend the class otherwise, with an excuse. Each absence without an excuse will cost 0.3 point. It is true that certain individuals are able to learn physics solely from a textbook and may think that lectures are unnecessary. It is also true that most part of the course follows the text book basically, but (1) more explanations which do not appear in a typical textbook will be given in class (2) some of the topics of the course are even not covered by the textbook. Participation will provide you the opportunity to gain more, to ask questions as well as clarifying explanations.

Grading Policy

The final scores will be based on the two exams and the homework with breakdown as follows:

Undergraduate Graduate

Homework 30% 25%

Midterm Exam 35% 30%

Final Exam 35% 30%

Extra Final Exam ----- 15%

The letter grades will be assigned based on the final scores. The approximate cutoffs are:

Grade A+ A A_ B+ B B_ C+ C C_ D+ D D-

Cutoff 95 90 80 75 70 65 55 50 41 38 35 32

* Please note that the scheduled exam date and above cutoffs are tentative. The instructor reserves the right to lower the cutoffs if deemed necessary. The cutoffs, however, will not be raised in any cases.

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