PHY5646 Spring 2002 Syllabus

Syllabus of PHY5646 Quantum Mechanics B, Spring 2002

Description and Goals for the Course: This is the second semester of a two-semester graduate level sequence on the fundamental concepts and applications of modern quantum mechanics; three graduate credit hours. Quantum Mechanics is the foundation of all branches of modern physics. The ultimate goal of this course is to introduce its central ideas and methodology to the students, and get them prepared for more advanced and specialized courses, and in particular, thesis research in both experimental and theoretical physics. In the meantime there are still a number of fundamental questions about Quantum Mechanics itself that remain unanswered and are the subject of active current research; the students will also be exposed to some of these problems.

Course Objectives: By the end of the second semester the students are expected to have learned to use a number approximate schemes to solve quantum mechanical problems that are not exactly soluble, and appreciated the importance of symmetry considerations in the solutions of quantum mechanical problems, either exact or approximate. They will also be introduced to the relativistic quantum mechanics which is the form of one-particle quantum mechanics that is compatible with special relativity, and its inadequacies; in attempting to fix these inadequacies one is eventually led to quantum field theory, which is the modern quantum theory of infinitely many interacting degrees of freedom that describes all fundamental particles and their interactions.

Prerequisites: PHY5645.

Textbook (required): J. J. Sakurai, Modern Quantum Mechanics, revised edition, Addison-Wesley, 1994. We will cover most parts of the last four chapters of this book this semester.

Grading: Final: 30%; Two Midterm Exams: 40% (20% each); Homework/Class Attendance: 30%. Tentative Grade Dividing Lines: A/A-: 80; A-/B+: 75; B+/B: 70; B/B-: 60; B-/C+: 55; C+/C: 50; C/D: 40.

Student Responsibilities: Active student participation is crucial to the success of this course. Specifically, they are expected to:

Attend lectures on time, and contribute to class discussions. Bonus points will be given to such contributions.
Finish and submit home works in time. Unless approved by the instructor in advance, late home works will not be accepted.
Participate in the midterm and final exams. Unless approved by the instructor in advance or in case of unforeseeable emergency, missed exams cannot be made up.

ADA Statement: Students with disabilities needing academic accommodation should: (1) register with and provide documentation to the Student Disability Resource Center; (2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.

Honor Code: Students are expected to uphold the Academic Honor Code published in the Florida State University Bulletin and the Student Handbook. The Academic Honor Systems of Florida State University is based on the premise that each student has the responsibility to (1) uphold the highest standards of academic integrity in the student's own work, (2) refuse to tolerate violations of academic integrity in the university community, and (3) foster a high sense of integrity and social responsibility on the part of the university community.

Course Topics:

Symmetry in Quantum Mechanics: Symmetries, conservation laws and degeneracies; discrete symmetries: parity, lattice translation, time-reversal, etc.; group theoretical description of symmetry symmetry operations and its application in quantum mechanics. (~ 3 lectures)
Approximation Methods: Time-independent perturbation theory; Variational methods; Time-dependent perturbation theory. (~ 6 lectures)
Identical Particles: Permutation symmetry; Symmetrization postulates; Two-electron systems. (~ 2 lectures)
Scattering Theory: The Lippman-Schwinger equation; The Born approximation; Optical theorem; Eikonal approximation; Method of partial waves; Time-dependent formulation of scattering, etc. (~ 8 lectures)
Relativistic Quantum Mechanics: The Klein-Gorden Equation; The Dirac Equation; Plane-wave solutions; Relativistic covariance; The hydrogen atom; etc. (~ 6 lectures)
Special Topics in Quantum Mechanics (time permits): Density operators, Berry's (geometrical) phases, Fractional statistics, Advanced topics on path integral formulation of quantum mechanics, Quantum theory of radiation field, etc.

Logistic Information:

Lectures: Tu., Th. 11:00--12:15, UPL 110.
Lecturer: Kun Yang; Office: 404 Keen and A306 Magnet Lab; Tel.: 4-5373 (magnet lab); 4-5208 (physics department); Homepage: magnet.fsu.edu/~kunyang; E-mail: kunyang@magnet.fsu.edu
Office hours: Tu., Th. 9-10 am, and by appointment. I am usually available on Tu. and Th. in my Keen Building office and in my Maglab office on other days. The students are encouraged use the office hours to discuss issues that are related to the course, or physics in general, with the instructor.
Course home page: www.physics.fsu.edu/courses/spring02/phy5646. Announcements related to the course, homework assignments, exams and their solutions will be posted here.
TA (grader of homework): Han Oh Lee; office: 221 Keen; phone: 4-7439; Email: hol1532@garnet.acns.fsu.edu
Home Work: Weekly, due in class on Thursdays. Problem sets and solutions will be available for pick up on Thursdays in class, and also on the course webpage.
Midterm Exams: There will be two midterm exams during class time, to be scheduled in mid February and late March (exact dates will be given at least two weeks in advance).
Final Exam: Monday, Apr. 22nd , 5:30pm-7:30pm.

Suggested Further Reading (not required): The textbook provides all the materials that will be covered this semester except for the part on Relativistic Quantum Mechanics. Materials on this part will be distributed to the students by the instructor. The following are a few other books that may be useful:

J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw-Hill (1964). This is a standard reference on the subject which will be covered this semester.
J. J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley (1967). The materials of this earlier book by the same author extend and compliment that of the textbook.
E. Merzbacher, Quantum Mechanics, Third Edition (1997). The discussion on scattering theory and identical particles of this book complements that of the textbook.