Physics 5450 - Introduction to Quantum Mechanics

Fall 2017 - David Ailion

David Ailion   
Office: JFB 218
Phone: 581-6973
Email: e-mail Dr. Ailion
Office Hours: M W 1:30-2:15 p.m. or by appointment
Mary Ann Woolf:   Contact her at  (phone - 581-4246) office - 205 JFB
Lectures: M W 12:55 - 2:50 p.m., JFB 325
Discussion: F: 12:55 - 2:55 p.m., JFB 325
Final Exam: Friday, December 12, 2017, 1:00 - 3:00 p.m.

Prerequisites: Physics 4420, Math 2250, Math 3150, Math 3160
Course TA
Ren-Bo Wang (email Ren-Bo)
Office Hours: JFB Rotunda: T 2:00-4:00 p.m., H 2:00-3:00 p.m.


Introduction to Quantum Mechanics, David J. Griffiths, 2nd. ed. (Pearson/Prentice Hall).


J.J. Sakurai, Modern Quantum Mechanics [Addison Wesley, 1994]
L. Landau and E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory
J.S.Townsend, A Modern Approach to QuantumMechanics [Univ.Science,2000]
A. Messiah, Quantum Mechanics [Dover, 1999]
L.I. Schiff, Quantum Mechanics (3d Ed.) [McGraw-Hill, 1968]
R. Shankar, Principles of Quantum Mechanics [Springer, 1994]
N. Zettili, Quantum Mechanics Concepts and Applications(2d Ed,) [Wiley 2009]
G.L. Squires, Problems in Quantum Mechanics (Cambridge Press,1995)

These books will be on reserve in the Marriott Library.


Physics 4420, Math 2250, Math 3150, Math 3160

Course Mechanics

The lectures will normally be given M W and will be followed by a discussion session on Fridays. The lecture notes will be posted on-line in the Physics 5450 Course website after each lecture. Even though the Class schedule lists Aug. 21 as the first day of classes we have decided to postpone the first class to Aug. 23, so that you may have the opportun

Homework will be assigned weekly, typically on Wednesdays and due at the beginning of class the following Wednesday. The assigned homework will be posted as soon as possible but not less than a week before the due date. Shortly after the Wednesday class, the homework solutions will be posted on-line in the Physics 5450 Course Website.

Once the homework solutions are posted, no late homework will be accepted. The homework is intended to be a learning experience, and you may get whatever help you need for them. You are encouraged to work with other students. Particular questions about upcoming homeworks can be addressed to the TA during his (or her) office hours, where he (or she) will be available to help you on an individual basis.

The discussion classes will be given on Fridays and will be led by the TA. The discussion will include the previous homework assignment (that has already been completed and handed in by you) and any other questions and problems that you have. The purpose of the discussion class is not to show you how to do the upcoming homework problems but is to help consolidate your understanding after you have worked on the problems. Also, the mid-term exams will be taken during the Friday discussion periods.

Hour Exams
There will be two mid-term exams. The first will be in early October and the second about four weeks later. Each exam will be closed book, with the exception that each student will be allowed to bring in a 4" x 6" card with whatever notes can be written on it. Each exam may be based on material covered in the lectures, the text, and the homework problems that have been assigned up to that point, including (though not necessarily limited to) the most recent material. There will be no makeup exams.

Final Exam
There will be a comprehensive final exam covering all the material of the course. It will be closed book except that a student can bring in a single 8 1/2 x 11 sheet of paper (2 sides). It will be given on the date specified in the Class Schedule. (See above.)

Homework - 20%
Mid-term Exams - 40%
Final Exam - 40%

Course Description
The course will start with a brief review of the experiments (blackbody radiation, photoelectric effect, Compton effect, etc.) that cannot be explained by classical physics, thereby providing the necessity for quantum mechanics.

This will be followed by a discussion of the wave function and its properties, leading to Schrödinger’s equation.

Next will be various applications of the 1-D Schrödinger equation (Infinite and finite square wells, free particle, harmonic oscillator, d-function potential, potential barriers).

This will be followed by a treatment of the mathematical formalism of quantum mechanics (Hilbert space, observables and Hermitian operators, eigenvalues and eigenfunctions, uncertainty principle, and Dirac bra and ket notation).

Next will be Schrödinger’s equation in 3-D. with solutions to the hydrogen atom [radial equation (Laguerre polynomials) and the angular equation (spherical harmonics)].

The next major topic will be angular momentum in QM – orbital and spin. This will include the Pauli spin matrices, Larmor precession, and addition of angular momenta (Clebsch-Gordon coefficients).

We next plan to introduce time-independent perturbation theory – both non-degenerate and degenerate. We will also study effects of magnetic fields – Zeeman effect, spin-orbit coupling, and the fine and hyperfine structure of the hydrogen atom. (Time-dependent perturbation theory will be discussed next semester in Physics 5460.)

Our next goal is to discuss the particular properties of systems containing more than one identical particle. Bosons and fermions will be introduced as well as the features of multi-particle wave functions, with consequences to the periodic table. Depending on time, this topic will be discussed may be postponed to the second semester (Physics 5460).

If there is time, I would like to present some applications of QM – specifically to nuclear magnetic resonance (NMR) and/or applications to solids (Kronig-Penny model, tight binding, nearly free approximations).

Important Dates

Last day to register without a permission code is Friday, August 25.
Last day to drop (delete) classes with no tuition penalties is Friday, September 1
Last day to add classes is Friday, September 1.
Last day to elect CR/NC options is Friday, September 1. Last day to withdraw from term length classes is Friday, October 20.

NOTE: It is now university policy that your courses will be irrevocably DROPPED if tuition is not paid on time!

Students with Disabilities

ADA Compliance: The University of Utah Department of Physics and Astronomy seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodation in this class, reasonable prior notice (at least one week prior) must be given to the instructor (DCA), to the Class Coordinator (Mary Ann Woolf), and to the Center for Disability Services,, at 1672 Olpin Union Bldg, (801) 581-5020 (V/TDD) to make arrangements of accommodation.


Cheating of any kind on an exam is a very serious violation of University rules and is unethical. Students caught cheating may receive a failing grade for the course and be sent on to the University Disciplinary Committee for further action. All teaching assistants and the administrative assistant for the course are to be considered proxies for Professor Ailion when you are dealing with them regarding this course. They are to be listened to and treated with respect at all times.

Recent Changes in Student Code

All students and faculty need to be aware of important changes in the Student Code that went into effect in the last couple of years. Students now have only 20 business days to appeal grades and other "academic actions" (e.g., results of comprehensive exams). The date that grades are posted on the web is considered the date of notification. A "business day" is every day the university is open for business, excluding weekends and University-recognized holidays. If the student cannot get a response from the faculty member after ten days of reasonable efforts to contact him or her, the student may appeal to the Department Chair if done within 40 days of being notified of the academic action. Students should definitely document their efforts to contact a faculty member.

Similarly, faculty members who discover or receive a complaint of academic misconduct (e.g., cheating, plagiarism) have 20 business days to "make reasonable efforts" to contact the student and discuss the alleged misconduct. Within 10 more business days the faculty member must give the student written notice of the sanction, if any, and the student's right to appeal to the college Academic Appeals Committee.

All students and faculty members are urged to consult the exact text of the Student Code if a relevant situation arises. The code is on the University web site at



 September 4  Labor Day
 October 8-15  Semester Break
 November 23-24  Thangsgiving Break

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