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Syllabus

Physics 555: Elementary Quantum Mechanics (Credit units: 3)

(Fall 2008)

Lecture Room: 104 Natural Sciences BLDG

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

Textbook: Introduction to Quantum Mechanics by David J. Griffiths, second edition (Pearson Prentice Hall)

Instructor: Dr. Ming Yu

Office: Room 242, Belknap Research Building

Office Hour: 2:00 pm – 5:00 pm (MW)

Phone Number: 502-852-0931

E-mail: m0yu0001@gwise.louisville.edu

Description: General concepts of quantum mechanics, Schrödinger equation and solutions in one- and three-dimensions., and introduction to angular momentum and identical particles.

Course Requirements: PHYS 300, 450, and 460.

Topics covered

1. Origin of Quantum Mechanics

1. Introduction

2. The Work of Planck-Blackbody Radiation

3. The Work of Einstein-Photoelectric Effect

4. The work of Bohr-A Quantum Theory of Atomic States

5. The Work of de Broglie -Waves Versus Particles

2. The Wave Function

1. The Schrödinger Equation

2. The Statistical Interpretation

3. Probability

4. Normalization

5. Momentum

6. The Uncertainty Principle

3. Time-Independent Schrödinger Equation

1. Stationary State

2. The Infinite Square Well

3. The Harmonic Oscillator

4. The Free Particle

5. The Delta-Function Potential

6. The Finite Square Well

4. Formalism

1. Hilbert Space

2. Observables

3. Eigenfunctions of a Hermitian Operator

4. Generalized Statistical Interpretation

5. The Uncertainty Principle

6. Dirac Notation

5. Quantum Mechanics in Three Dimensions

1. Schrödinger Equation in Spherical Coordinates

2. The Hydrogen Atom

3. Angular Momentum

4. Spin

6. Identical Particles

1. Two-Particle Systems

2. Atoms

3. Solids

4. Quantum Statistical mechanics

Homework

Homework assignments will be distributed at beginning of each chapter. Chapter tests will be arranged near the end of each chapter. The corresponding due dates for Homework and Chapter test will be written on the Homework assignments and Chapter tests. Homework assignments and Chapter tests 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 October 10.

Grading Policy

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

Homework 20% Chapter Test 10% 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 90 85 78 70 65 60 50 45 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.

Syllabus

Physics 622: Quantum Mechanics II (Credit units: 3)

(Spring 2008)

Lecture Room: 306 Natural Sciences BLDG

Lecture Time: 4:00 pm-5:15 pm (Tues & Thurs)

Textbook: Quantum Mechanics: Concepts and Applications by N. Zettili (John Wiley & Sons)

Reference books: 1. Modern Quantum Mechanics by J. J. Sakurai (2nd Edition, The Benjamin/Cummings, CA, USA, 1994); 2. Principles of Quantum Mechanics by R. Shankar (New York, Coulomb Hamiltonian, World Scientific Sep 1, 1994).

Instructor: Dr. Ming Yu

Office: Room 242, Belknap Research Building

Office Hour: 10:00 am – 12:00 pm (MW)

PhoneNnumber: 502-852-0931

E-mail: m0yu0001@gwise.louisville.edu

Description: Nonrelativistic quantum mechanics (continue) including angular momentum theory, perturbation theory, systems of identical particles and symmetries, and scattering theory.

Course Requirements: PHYS 556, 561, 605, and 621.

Topics covered:

7. Angular Momentum Revisited

6. General angular momentum

1. General formalism of angular momentum

2. Eigenstates and eigenvalues of the angular momentum operator

3. Matrix representation of angular momentum

7. Spin angular momentum

1. Experimental evidence of the spin

2. General theory of spin

8. Rotation and Addition of Angular Momentum

a. Rotation in quantum mechanics

i. Finite rotations

ii. Infinitesimal rotations

iii. Euler rotations

iv. Representation of the rotation operator

v. Rotation matrices and the spherical harmonics

b. Addition of angular momenta

i. Addition of two angular momenta: general formalism

ii. Transformation between bases: Clebsch-Gordan coefficients

iii. Coupling of orbital and spin angular momenta

iv. Spin-spin coupling

c. Scalar, spinor and vector Fields

3. Perturbation Theory

d. Time-independent perturbation theory

i. Nondegenerate perturbation theory

ii. Degenerate perturbation theory

e. Fine structure and Zeeman effect

i. Spin-orbital coupling

ii. Relativistic correction

iii. The fine structure of hydrogen

iv. The anomalous Zeeman effect

f. Time-dependent perturbation theory

i. The pictures of quantum mechanics

ii. Transition probability

9. System of Identical Particles

a. Many-particle systems

i. Schrödinger equation for many-particle systems

ii. Interchange symmetry

iii. Systems of distinguishable noninteracting particles

b. Systems of identical particles (permutation symmetry)

i. Identical particles

ii. Exchange degeneracy

iii. Summarization postulate

iv. Constructing symmetric and antisymmetric functions

v. The Pauli exclusion principle

c. Two-fermions system

i. LS-coupling and JJ-coupling

ii. The helium atom

d. Systems of more than two fermions

i. Many-particle interaction

ii. Hartree-Fock approximation

10. Scattering Theory

5. Scattering and cross section

1. Connecting the angles in the lab and CM frames

2. Connecting the Lab and CM sections

a. Scattering amplitude of spinless particles

i. Scattering amplitude and differential cross section

ii. Scattering amplitude

b. Born approximation

i. The first born approximation

ii. Validity of the first born approximation

c. The method of partial waves

i. Particle wave analysis for elastic scattering

ii. Particle wave analysis for inelastic scattering

We may discuss some additional topics in mechanics as time allows.

Syllabus

Physics 622: Quantum Mechanics II

(Spring 2008)

Lecture Room: Room 105, Natural Science Building

Lecture Time: 4:00 pm-5:15 pm (Tues & Thurs)

Textbook: 1. Modern Quantum Mechanics by J. J. Sakurai (2nd Edition, 1994, Published by The Benjamin/Cummings, CA, USA);

2. Quantum Mechanics (2 vol. set) by Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloe, (2nd Revised and enlarged edition 1977, Published by Hermann, Paris, France)

Instructor: Dr. Ming Yu

Office: Room 242, Belknap Research Building

Office Hour: 10:00 am – 12:00 pm (MWF)

Phone number: 502-852-0931

E-mail: m0yu0001@gwise.louisville.edu

Description: Nonrelativistic quantum mechanics including Hilbert space formalism, Schrodinger and Heisenberg representations, angular momentum theory, perturbation theory, scattering theory, systems of identical particles and symmetries, and applications.

Topics covered

11. Angular Momentum revisited

12. Rotation and Angular Momentum

13. Coupling of two angular Momentum

14. Scalar, Spinor and Vector Fields

15. Spin-dependent Interactions

16. Polarization of Particles with Spin

17. System of Particles

18. LS-coupling and jj-coupling

19. Two Fermion System in LS-coupling

20. The Helium Atom

21. Configuration Mixing

22. Systems of more than two Fermions

23. calculation of Single-particle Wave Function (Hartree-Fock Approximation)

24. Time-dependent Perturbation Theory

25. Scattering

26. The Method of partial Waves

Midterm Exam (March 2)

We may discuss some additional topics in mechanics as time allows.

Homework

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 Oct. 11.

Grading Policy

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

Homework 25% Midterm Exam 35% Final Exam 40%

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 94 90 84 77 72 67 63 60 57 55 53 50

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.

Teaching goal:

1) Quantum Mechanics is one of the difficult courses and much new knowledge compared with the traditional physics for the graduate students because they thought it is too unrealistic and abstract. So in order to bring their interesting on it and master the principle of QM after learning, I tried to do followings:

2) Let them ask questions on the class off the class as possible as they can. Encourage them to raise their questions and try to answer these questions as possible as I can. Let them feel free to ask any kind of question and encourage them do not postpone their questions so that they can follow the process of the class and do not save their question in their mind. By doing so, students can clear up stones and break through to the key concept of QM. Once they really understand what they have learnt they become interested in QM.

3) Base on the text book but bring deeper and wider knowledge referring other good QM books for them so that they can extend their knowledge of QM not only from reading the textbook but also from the class. In this way, they would feel like to attend the class and pay attention on the class, making notes and

4) Make a clear syllabus and also in each class, briefly review what have learnt in last class and make a link between the last class and the present class. In such summary, students will remind what they have learnt last class and bring an interesting and question for the present class. Therefore they will pay more attention on the class.

5) On the class not only teach the concept and topic but also talk about how the equations and conclusion come from by proving and driving in details. In such a way, students will have more clear understand what is the principle of QM, how the QM theory set up, also training them how to solve the QM problems using mathematical tools, physical principle and their background knowledge.

6) Assign homework and grade the homework for students so that they can accept what they learnt on the class and do more excises to solve the problems themselves. Also by grading their homework, I can get the feedback about more clear understand each student’s level and what is needed to improve. I also point out where they did wrong and what is the correct answer so that they known what they need to improve themselves.

Survey of Phys 622 Quantum Mechanics (04/172008)

1. (a) What do you think of the topics covered in the QM class? Are they interesting topics?

(b) Which topics do you like?

(c) Which you do not like?

(d) Do you have suggestions on the topics covered?

2. (a) What do you think of the textbook?

(b) Does it help you to understand the principles of QM and to solve QM problems?

(c) Do you have suggestions on the selection of textbook?

3. (a) What do you think of the homeworks assigned for you? Easy or challenge?

(b) Do you think that my grading on your homework helps you to master QM knowledge and to improve your skill in solving QM problems?

4. (a) What do you think of the QM before taking the course? Was it difficult?

(b) What do you think of the QM after finishing the course? Is it still difficult for you?

(c) Do you feel happy with learning QM now?

5. (a) How long did it take for you to finish the midterm exam at home?

(b) If the exam is taken on the class, please estimate how long can you finish it?

(c) Do you think it would be difficult for you if the exam is taken on the class?

6. Any other suggestions?

Thank you for your collaboration.

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