Catalog description

Schrodinger’s equation and Hilbert spaces. Symmetry and conversation laws. Path integral quantization. Quantum theory of angular momentum. Systems of identical particles and many-electron atoms. Perturbation theory. Nonrelativistic scattering.

3 credit hours

Where and when

Required text

Grading scheme

Your grade will be based on the cumulative points you earn from assignments, a midterm exam, and a final exam, weighted as follows.

The numerical score (out of 100) will be converted to a letter grade with a corresponding grade point value, following the UM +/– grading system adopted in Fall 2011. The conversion is carried out by matching to the ranges shown in the table below.

Class attendance — Regular attendance is strongly encouraged. Some material presented in lecture may not appear in your textbook. During class, I will sometimes present worked problems, give hints and tips about the homework, and provide guidance about where to focus your studies for the tests and exams.

Homework — Homework assignments will be due in class. Late assignments will be penalized at the rate of 20% per day.

Learning objectives

Students will become acquainted with the formalism of non-relativistic, few-particle quantum mechanics. They will develop a deeper appreciation for the mathematical structure of quantum theory and the important role that symmetry plays. They will learn to formulate quantum problems in terms of both Schrödingers wave equation and Heisenberg’s matrix mechanics. They will master a variety of exact and approximate solution strategies.

Topics likely to be covered

Fundamental Concepts (Sakurai Ch 1.1–1.7) — Hilbert space; kets and bras; matrix representations, change of basis, wave functions in position and momentum space

Quantum Dynamics (Sakurai Ch 2.1–2.5,2.7) — time evolution, Schrödinger versus Heisenberg picture, simple harmonic oscillator, Schrödinger’s wave equation, potentials and gauge transformations

Theory of Angular Momentum (Sakurai Ch 3.1–3.8) — rotations and angular-momentum commutation relations, spin-half systems, relationship between SO(3) and SU(2), eigenstates of angular momentum, Schrödinger equation for central potentials

Symmetry in Quantum Mechanics (Sakurai Ch 4.1–4.4) — symmetries, conservation laws, degeneracies, parity, space inversion, translation and crystal momentum, time-reversal

Approximate Methods (Sakurai Ch 5.1-5.4) — time-independent perturbation theory, variational methods

Identical Particles (Sakuria Ch 7.1–7.4) — permutation symmetry, symmetry postulate, two-electron system, helium atom

Academic integrity and honesty

Students are expected to adhere to the University of Mississippi Creed and the Standards of Honesty as described in Policy Code ACA.AR.600.001 and the M Book.

Students are reminded that cheating in any form will not be tolerated. Performance on all tests and assignments shall represent the individual work of the student. Those who violate the Standards of Honesty will be reported and subject to the appropriate sanction, which may include expulsion from the University.

Nondiscrimination policy

The University complies with all applicable laws regarding affirmative action and equal opportunity in all its activities and programs and does not discriminate against anyone protected by law because of age, color, disability, national origin, race, religion, sex, sexual orientation, handicap, or status as a veteran or disabled veteran.

Policies and procedures for students with disabilities

It is University policy to provide, on a flexible and individual basis, reasonable accommodations to students who have disabilities that may affect their ability to participate in course activities or meet course requirements. Students with disabilities should contact the Office of Student Disability Services (662-915-7128 or sds@olemiss.edu) to discuss their individual needs.

Examinations and last week of class

Regulations governing all examinations — A student’s failure to appear for an examination without an acceptable excuse,inability to present valid identification,absence from the room during the course of an examination without the consent of the examiner, or attempting any portion of an examination without submitting his or her answers shall result in failure of the examination. Tardiness beyond 15 minutes forfeits a student’s right to an examination.

Final examinations — A final examination, to be given at the time posted in the examination schedule, is required in each undergraduate course, unless the appropriate chair and dean have approved an exception. A student who has three or four final examinations in one day may arrange with the course instructor to take the noon or 7:30 p.m. examination at another time. In order to give a final examination at any time other than that shown in the posted examination schedule, an instructor must have prior approval of the department chair and dean.

Last week of class — The following guidelines exist to allow sufficient time for students and instructors to prepare for final examinations. These guidelines apply to the week preceding final examinations for undergraduate courses held during Fall and Spring semesters.

• During the period of Wednesday through Friday of the last week of class, instructors are not to give exams, tests, or quizzes that contribute more than 10% of the final grade for a class. An instructor can obtain approval of the department chair and dean to give an exam, test, or quiz, of this weight, during this three day period. Instructors should return graded work and/or inform students of their grades on exams, tests, or quizzes prior to the beginning of finals week.

• Exceptions to the above statement are automatically made for lab-based courses, technical writing courses, seminar courses that assign a term paper, and senior design courses that assign a multi-faceted project in lieu of a final exam. Major projects of the above types, which contribute more than 10% of the final grade and which are due during this Last Week period, should be assigned in the syllabus at the beginning of the semester and any substantial change in the assignment should be made known to students before the drop deadline.