Syllabus

Physics 622: Quantum Mechanics II (Spring 2014)

Class number: 3493 (Credit units: 3)

Lecture Room: 104 Natural Sciences BLDG

Lecture Time: 4:00 pm-5:15 pm (Tuesday and Thursday)

Textbook: Quantum Mechanics: Concepts and Applications

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

Reference book: (1) Principles of Quantum Mechanics

by Ramanurti Shankar (Plenum Press);

(2) 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 – 3:00 pm (Tuesday and Thursday)

Phone Number: 502-852-0931

E-mail:

Web site: http://www.physics.louisville.edu/yu/

Description: This course is the second part of the two-semester course of quantum mechanics (Phys 621 and Phys 622). This course (Phys 622) will cover the topics of the hydrogen atom, Zeeman effect, the rotations, addition of angular momenta, identical particles for systems with more than one particle, 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 improve critical thinking skills and problem-solving skills. The key elements related to this goal will include: introducing the identical particles in quantum mechanics, dealing with the rotation and 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. Depending on time available, we might possibly cover the optional topics as listed in the “Topics covered”. 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 555, 556 and 621.

Topics covered

  1. Rotations (The 1st and 2nd sections in Chapter 7)

1.1  Infinitesimal Rotation

1.2  Finite Rotation

1.3  Properties of the Rotation Operator

1.4  Representation of the Rotation Operator

1.5  Rotation Matrices and the Spherical Harmonics (Optional)

  1. Addition of Angular Momenta (The 3rd section in Chapter 7)

2.1  Addition of Two Angular Momenta

2.2  Calculation of the Clebsch-Gordan Coefficients

2.3  Coupling of Orbital and Spin Angular Momenta

2.4  Addition of More Than Two Angular Momenta

2.5  Rotation Matrices for Coupling Two Angular Momenta (Optional)

  1. Scalar, Vector, and Tensor Operators (The 4th section in Chapter 7-Optional)

3.1  Scalar Operators

3.2  Vector Operators

3.3  Tensor Operators

  1. Identical Particles (Chapter 8)

4.1  Many-Particle Systems

4.2  Systems of Identical Particles

4.3  The Pauli Exclusion Principle

4.4  The Exclusion Principle and the Periodic Table

4.5  Quantum Statistical Mechanics (Optional)

5. Time-Independent Perturbation Theory (The 2nd section of Chapter 9)

5.1  Nondegenerate Perturbation

5.2  Degenerate Perturbation Theory

5.3  The Fine Structure of Hydrogen

5.4  The Anomalous Zeeman Effect

6.  The Variational Principle (The 3rd section of Chapter 9)

6.1  General Theory

6.2  The Ground State of Helium

6.3  The Hydrogen Molecule Ion

7.  The Wentzel-Kramers-Brillouim Method (The 4th section of Chapter 9-Optional)

7.1 General Formalism

7.2 Bound States for Potential Wells with No- One-, and Two-Rigid Walls

7.3 Tunneling Through a Potential Barrier

8.  Time-Dependent Perturbation Theory (Chapter 10)

8.1  The Picture of Quantum Mechanics

8.2  Time-Dependent Perturbation Theory

8.3  Adiabatic and Sudden Approximation (Optional)

8.4  Interaction of Atoms wit Radiation (Optional)

8.5  Spontaneous Emission (Optional)

9.  Scattering (Chapter 11)

9.1  Scattering and Cross Section

9.2  cattering Amplitude of Spinless Particles

9.3  The Born Approximation

9.4  Partial Wave Analysis (Optional)

9.5  Scattering of Identical Particles

Homework

Homework assignments will be distributed at beginning of each week. The Homework includes general 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.

Exams

There will be a midterm exam and a final exam. The midterm exam is scheduled on March 6/18, and the final exam is scheduled on April 17/24. The midterm exam will only have a “take-home” section. The final exam will have an “in-class” and a “take-home” section. They are weighted as half and half, 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 0.5 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:

Homework 30%

Midterm Exam 35%

Final Exam 35%

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 98 90 82 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.