This page is https://web.physics.wustl.edu/~wimd/index523-22.html
Last updated 2022-Aug-15

Physics 523: Quantum Mechanics I, Fall 2022

Teaching

Provides a treatment of quantum mechanics based on experimental observations that clarify its mathematical framework and interpretation as developed by Dirac while clarifying the link with wave mechanics. Discussion of continuous symmetries: translation and rotation invariance, quantum dynamics including propagators and path integrals, quantum theory of angular momentum and rotation groups, Bell’s inequality. Emphasis is on applications and (numerical) solutions to problems of current physical interest. Prerequisite: Phys 217 or 471 or equivalent.

Practical matters

The course meets on MWF from 10-10:50am in Crow 206. Class will start on Monday, August 29. The enrollment in this class is such that it allows an interactive and meaningful exposure to the main ideas and techniques of Quantum Mechanics. I look forward to meeting you on August 29!

Instructor:	Willem Dickhoff Office: Compton 371; Email: wimd@wuphys.wustl.edu Office hours: Thursday TBA and by email appointment
AI:	TBA Office: ; Phone: 5-xxx; Email: Office hours: Thursday ... and by email appointment

Books

Course Textbooks:

Required: Modern Quantum Mechanics (Cambridge;3rd edition) (2021) by Sakurai and Napolitano, ISBN-13: 978-1-108-47332-4 (hardcover).
We will cover a substantial fraction of the material in this book during the Fall Semester. It will also be used in the Spring Semester.

Recommended: Quantum Mechanics: Fundamentals (Springer; 2nd edition) (2004) by Gottfried and Yan, ISBN-13: 978-0387220239 (softcover). This book is not as friendly but is written at a higher level. Students interested in theory are advised to consider this book in addition to Sakurai.

Recommended: Lectures on Quantum Mechanics (Cambridge; 2nd edition) (2015) by Weinberg, ISBN-13: 978-1-107-11166-0 (hardcover).
Contains the insights of a master.

You are expected to have a copy of one of these books available at all times.

Additional books that you should consult once in a while:
Messiah (available as ebook)
Cohen-Tannoudji et al. (3 volumes)
Landau & Lifshitz
Baym
Dirac
All are expected to be on reserve in the physics library.

Course outline

The course is defined by the material discussed in the lectures and reviewed in the problem sets. A preliminary schedule is given below with references to the Sakurai book. It includes the covered material in the book, the subject, date of class, and the homework schedule.

Lecture		Subject material	meeting date	Hwk
#1	Intro course etc.	Reminder of wave mechanics	8/29/2022
#2	Chapter 1.1-2	First analysis Stern-Gerlach experiment	8/31/2022
#3	Chapter 1.2-3	Hilbert space; Dirac notation; kets, bras, operators	9/2/2022	Problems Set 1
	Labor Day	No class	9/5/2022
#4	Chapter 1.3	Unitary transformations; Eigenvalues & eigenvectors	9/7/2022
#5	Chapter 1.3-4	Measurement postulates (Dirac)	9/9/2022	Problems Set 2 Homework due Set 1
#6	Chapter 1.4	More Stern-Gerlach analysis	9/12/2022
#7	Chapter 1.4	Compatible observables	9/14/2022
#8	Chapter 1.4-5	Incompatible observables and basis transformations	9/16/2022	Problem Set 3 Homework due Set 2
#9	Chapter 1.4	Uncertainty relations	9/19/2022
#10	Chapter 1.6	Continuous observables; position and momentum	9/21/2022
#11	Chapter 1.6	Quantization; Familiar commutator; Translations	9/23/2023	Problem Set 4 Homework due Set 3
#12	Chapter 1.7	Coordinate space; Wave functions	9/26/2022
#13	Chapter 2.1	Equations of motion	9/28/2022
#14	Chapter 2.2	Schroedinger picture vs Heisenberg picture	9/30/2022	Problem Set 5 Homework due Set 4
#15		Measurement S. vs. H.picture	10/3/2022
#16	Chapter 2.2	Ehrenfest and classical equations; time-energy uncertainty relation	10/5/2022
#17	Chapter 2.3	Illustration with harmonic oscillator	10/7/2022	Problem Set 6 Homework due Set 5
	Fall Break	No class	10/10/2022
#18	Review		10/12/2022
#19	Midterm	From 9-11 or 10-12	10/14/2022
#20	Chapter 2.3	More harmonic oscillator; wave functions	10/17/2022
#21	Chapter 2.3	Harmonic oscillators in classical physics and examples	10/19/2022
#22	Chapter 3.1	Angular momentum; rotations	10/21/2022	Problem Set 7 Homework due Set 6
#23	Chapter 3.1-2	Consistency of rotations and commutation relations of angular momentum; Spin 1/2 and rotations	10/24/2022
#24	Chapter 3.5	Eigenvalues and eigenstates of angular momentumno class	10/26/2022
#25	Chapter 3.2	Pauli two-component formalism	10/28/2022	Problem Set 8 Homework due Set 7
#26	Chapter 3.2,3.6	Rotations in two-component formalism; orbital angular momentum	10/31/2022
#27	Chapter 3.6	Orbital angular momentum; spherical harmonics	11/2/2022
#28	Chapter 3.6	Preparation for problems with spherical symmetry; Schroedinger equation	11/4/2022	Problem Set 9 Homework due Set 8
#29	Chapter 3.7	Schroedinger equation for central potentials; free particles; spherical Bessel functions; limits of wave functions near the origin and at infinity (bound states)	11/7/2022
#30	Chapter 3.7	3D Harmonic oscillator alternative treatment	11/9/2022
#31		continued; states and wave functions	11/11/2022	Problem Set 10 Homework due Set 9
#32		Numerical solution of bound-state eigenvalue problems with spherical symmetry	11/14/2022
#33	Chapter 3.7	Hydrogen atom alternative treatment	11/16/2022
#34	Chapter 3.7	Atoms; Hydrogen in momentum space and (e,2e) reaction	11/18/2022	Problem Set 11 Homework due Set 10
#35	Chapter 3.8	Addition of angular momentum	11/21/2022
	Thanksgiving break	no class	11/23/2022
	Thanksgiving break	no class	11/25/2022
#36	Chapter 3.8	Continued	11/28/2022
#37	Chapter 3.10	Bell's inequality	11/30/2022
#38	Chapter 3.3 and 3.11	Euler angles; Spherical harmonics & rotation matrices	12/2/2022	Problem Set 12 Homework due Set 11
#39	Chapter 3.11	Tensor operators and angular momentum	12/5/2022
#40	Chapter 3.11	Wigner-Eckert theorem	12/7/2022
#41	Chapter 3.11	continued	12/9/2022	Homework due Set 12
	Presentations	TBA	12/15/2022
	Presentations	TBA	12/16/2022
	Presentations	TBA	12/19/2022

Grading and format of the course

FORMAT OF COURSE:

Three meetings per week (MWF)

Participate in class!

Try to read appropriate material for each class (review or preparation).

Homework assignments every week to be turned in a week later in pdf form on Canvas.

Homework graded and returned a week later.

Office hours to be determined

AI will be available for office hours as well

COURSE GRADE:

12 Homework sets for a total of ~40% (includes some numerical work)

Midterm exam for a total of ~30%

Final project: preparation and presentation of about half an hour mini lecture to the class about quantum material not previously discussed in class for a total of ~30%

Participation in class and improved performance over the semester will contribute as well

Students are encouraged to form study groups and discuss the homework with each other, but each student must write his or her own solutions.

Course materials

Additional material will be uploaded on the Canvas page

Course Evaluation

During the evaluation period you can supply your evaluation of the course at the course evaluation website.