Physics 5450, Introduction to Quantum Mechanics Fall Semester ...

Physics 5450, Introduction to Quantum Mechanics Fall Semester, 2017 SYLLABUS Professor: Office: Phone: Email: Office Hours: Class: Lectures: Discussion:

David C. Ailion 218 JFB (801) 581-6973 [email protected] Room 218 JFB, MW 2:55-3:45 PM or by appointment MWF JFB 325 MW 12:55 -2:50 PM F 12:55 1:45 PM

Class Coordinator: Mary Ann Woolf, Room 205 JFB Phone: (801) 581-4246 Email: [email protected] Final Exam:

Monday, Dec 12, 2017, 1:00-3:00 PM

TA: TA’s Office Hrs: TA's Email:

Ren-Bo Wang JFB Rotunda: T 2:00-4:00 p.m.; H 2:00-3:00 [email protected]

Text:

Introduction to Quantum Mechanics by David J. Griffiths (2nd Ed.) [Pearson/Prentice Hall 2005]

References: 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. Prerequisites: Physics 4420, Math 2250, Math 3150, Math 3160

Course Mechanics: Lectures:

Homework:

The lectures will normally be given MW 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 opportunity to watch the solar eclipse that day Homework will be assigned weekly, typically on Wednesdays and due at the beginning of class the following Wednesday. The homework assignments 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.

Discussion:

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 midterm exams will be taken during the Friday discussion periods.

Hr Exams:

There will be two mid-term exams. The first will be in early October (probably just before the Fall break) 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.) in Room 325 JFB.

Grading:

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

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, http://disability.utah.edu, at 1672 Olpin Union Bldg, (801) 581-5020 (V/TDD) to make arrangements of accommodation.

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, δ-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 multiparticle wave functions, with consequences to the periodic table. Depending on time, this topic will be discussed or 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).