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Last updated 2025-Jan-1

Physics 524: Quantum Mechanics II, Spring 2025

Teaching

The course meets on MWF from 10-11am in Crow 206. Class will start on Monday, January 13.

Instructor:	Willem Dickhoff Office: Compton 371; Email: wimd@wuphys.wustl.edu Office hours: MWF 11:30-12:30 and appointment
TA:	Office: Compton 374 ; Email: @wustl.edu Office hours:Th

Books

Course Textbook:	Modern Quantum Mechanics (Cambridge; 3nd edition) (2021) by Sakurai and Napolitano, ISBN-13: 978-1-108-47322-4 (hardcover). We will cover an appropriate fraction of the material in this book during the Spring Semester. You should have a copy of this book available at all times. Sakurai is user friendly but the books by Gottfried and Weinberg are certainly worth paying attention to as well.
Other useful books:	Additional books that you should consult once in a while are: Messiah Gottfried and Yan Weinberg Cohen-Tannoudji et al. Sakurai Gottfried Merzbacher Landau & Lifshitz Baym Dirac Dickhoff and Van Neck (for many-fermion and many-boson material)

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. It includes the covered material in the books, the subject, date of class, and the homework schedule. Most reading assignments are from Sakurai (S) while a few chapters from Dickhoff & Van Neck (DVN) will be made available as well.

Lecture	Chapters Sakurai	Subject material	meeting date	Hwk
#1		Review of Angular Momentum	1/13/2025
#2	S3.2	Rotations spin 1/2 with two-component formalism	1/15/2025
#3	S3.3	Euler rotations	1/17/2025	Problem Set 1
		MLK day	1/20/2025
#4	S3.11	Vector Operator	1/22/2025
#5	S3.11	Cartesian and Spherical Tensors; Product of Tensors	1/24/2025	Homework due Set 1 Problem Set 2
#6	S3.11	Wigner-Eckart and Projection Theorem	1/27/2025
#7	S4.1.1-3	Symmetries: parity	1/29/2025
#8	S4.2	Parity and angular momentum; Parity conservation?	1/31/2025	Homework due Set 2 Problem Set 3
#9	S4.4	General issues preparing for time reversal	2/3/2025
#10	S4.4	Time reversal and angular momentum	2/5/2025
#11	S4.4	Time reversal and spin 1/2	2/7/2025	Homework due Set 3 Problem Set 4
#12	S6.4	Ingredients to calculate scattering cross sections	2/10/2025
#13	S6.4.4	Radial Schroedinger equation and partial waves	2/12/2025
#14		Bound states from the computer; Numerov for the continuum	2/14/2025	Homework due Set 4 Problem Set 5
#15	S6	Scattering: Wave packets --> follow Weinberg	2/17/2025
#16	S6	Integral form of Schroedinger equation	2/19/2025
#17	S6	Explicit wave packet example; Scattering amplitude and cross section; Optical Theorem	2/21/2025	Homework due Set 5 Problem Set 6
#18	S6	Born approximation; square well; low-energy scattering and bound states; Examples	2/24/2025
#19	S6 & S5.1	Examples; Perturbation theory; examples	2/26/2025
#20	S5.2	Degenerate-state perturbation theory	2/28/2025	Homework due Set 6 Problem Set 7
#21	S5.3	Degenerate-state perturbation theory examples	3/3/2025
#22	Review		3/5/3025
#23	Midterm	9:00-11 or 10-12	3/7/2025
	Spring break		3/8-16/2025
#24	S5.4	Variational principle	3/17/2025
#25	S5.5	Time-dependent perturbation theory; Golden rule	3/19/2025
#26	S5.7	Two-level systems	3/21/2025	Homework due Set 7 Problem Set 8
#27	S6	CPT; Examples and scattering of identical particles	3/24/2025
#28	S7.1-5 Ch.1 DVN	Identical particles	3/26/2025
#29	S7.7 Ch.2 DVN	Second quantization	3/28/2025	Homework due Set 8 Problem Set 9
#30	Ch.3 DVN	Fermions; Independent particle model	3/31/2025
#31	Ch.3 DVN	Atoms and nuclei	4/2/2025
#32	Ch.5 DVN	Statistical mechanics and identical particles	4/4/2025	Homework due Set 9 Problem Set 10
#33	Ch.5 DVN	Bose-Einstein condensation and in traps	4/7/2025
#34	Ch.5 DVN	Bose-Einstein condensation in traps; Fermi Gas	4/9/2025
#35	S2.7	Minimal coupling; Landau levels	4/11/2025	Homework due Set 10 Problem Set 11
#36	S2.7	Aharonov-Bohm; Free fields	4/14/2025
#37	S7.8	Quantize Maxwell's equations; Many-bosons	4/16/2025
#38	S7.8	Photons; coupling to charged particles	4/18/2025	Homework due Set 11
#39		Photon emission; Lifetime; absorption cross section	4/21/2025
#40		Photoelectric effect; Planck	4/23/2025
#41		TBA	4/25/2025
	Review	Compton 241	5/2/2025
	FINAL EXAM	Crow 206 from 10:30-12:30	5/5/2025

Grading and format of the course

FORMAT OF COURSE:

Three meetings per week in Crow 206.

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

Class participation and presence is important.

Homework assignment approximately every week to be turned in a week as a pdf on the Canvas or Gradescope page for the course. Homework to be graded within the following week.

COURSE GRADE:

11 homework including one numerical project for a total of ~40% of course grade

Midterm exam for a total of ~30%

Final exam for a total of ~30%

Students are encouraged to form study groups and discuss the homework with each other, but each student must write his or her own solutions. You may be asked to discuss solution strategies of homework problems during class.

Learning goals

Acquire the skills to apply all aspects on angular momentum in quantum mechanics including the use of the Wigner-Eckert theorem
Apply the consequences of discrete symmetries like parity and time reversal to transitions between quantum states
Apply various approximation methods including perturbation theory (both nondegenerate and degenerate) and the variational principle
Acquire the skills to solve scattering problems on the computer generating phase shifts and differential cross sections
Learn how to work with many-particle states consisting of identical fermions and bosons including the method of second quantization
Learn to quantize the free electromagnetic field thereby generating photon states and incorporate the EM field in the Schrodinger equation
Calculate electromagnetic transition probabilities between atomic states
Understand the details of the photo-electric effect and Planck's radiation law

Important University policies and guidelines

Course Evaluation

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