Syllabus

Physics 621: Quantum Mechanics I (Fall 2012)

(Creditunits: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)

PhoneNumber: 502-852-0931

E-mail:

Web site:

Description

This course is the first part of the two-semester course of quantum mechanics (phys 621 and phys 622). This course (Phys 621) will cover the general concepts of quantum mechanics, Schrödinger equation and solutions in one- and three-dimensionproblems, the general angular momentum, as well as the rotations.A mathematical background of linear algebra, differential equations, and partial differential equations is strongly required in the course.

Goal

The goal of this course will be to reviewbasic concepts of quantum mechanics, to improve critical thinking skillsandproblem-solving skills. The key elements related to this goal will include: reviewing the mathematical tools of quantum mechanics, re-discussing the formal foundation of quantum mechanics, and then dealing with the exact solutions of the Schrodinger equation and the properties of angular momentum. 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 studentsor 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 and embedded in exam questions, etc.).

Course Requirements

PHYS 555 and 556.

Topics covered

  1. Postulates of Quantum Mechanics and Related Mathematical Tools (Chapters 2& 3)
  2. Introduction
  3. The Basic Postulates of Quantum Mechanics
  4. The State ofSystem and Wave Functions
  5. Observables and Operators
  6. Measurement in Quantum Mechanics
  7. Time Evolution of the System’s State
  8. Symmetries and Conservation Laws
  9. One-Dimensional Problems(Chapter 4)
  10. Introduction
  11. Properties of One-Dimensional Motion
  12. The Free Particle: Continuous States
  13. The Potential Step
  14. The Potential Barrier and Well
  15. The Infinite Square Well Potential
  16. The Finite Square Well Potential
  17. The Harmonic Oscillator
  18. Angular Momentum(Chapter 5)
  19. Introduction
  20. Orbital Angular Momentum
  21. General Formalism of Angular Momentum
  22. Matrix Representation of Angular Momentum
  23. Spin Angular Momentum
  24. Eigenfunctions of Orbital Angular Momentum
  25. Three-Dimensional Problems (Chapter 6)
  26. 3D Problems in Cartesian Coordinates
  27. 3D Problems in Spherical Coordinates (Central Force Problems)
  28. The Hydrogen Atom
  29. Effect of Magnetic Field on Central Potentials
  30. Rotations (Optional)

5.1 Rotations in Classical Physics (Chapter 7.1)

5.2 Rotations in Quantum Mechanics (Chapter 7.2)

Homework

Homework assignmentswill 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 answersbut intermediate steps. The corresponding due dates for Homework will be written on the Homework assignments. Homework assignmentswill 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 11, 2012, and the final exam is scheduled on December 4-11, 2012.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 alsotrue that most part of the course follows the text book basically, but (1) more explanations which do not appear in a typical textbookwill be given in class(2) some of the topicsof 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:

GradeA+AA_B+BB_C+CC_D+DD-

Cutoff959080757065555041383532

* 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.