Department of Physics
University of Illinois at UrbanaChampaign
Room 2119 ESB, MC704,
1110 W Green St, Urbana, IL 618013080
Phone: 2173334409
Fax: 2172447704
Email: efradkin@illinois.edu
http://eduardo.physics.illinois.edu/homepage/
Time: Tuesdays and Thursdays 2:00 pm  3:20 pm
Place: Rm 276 Loomis Lab.
CRN: 36784
Credit: 1 unit.
Office Hours: Wednesdays 2:30 pm  3:30 pm (by zoom) (registered students were given the link in an email)
TA: Mr. Zejun Liu
Office: TBA
Office Hours: Thursdays 4:00 pm to 5:00 pm (by zoom) (registered students were given the link in an email)
Email: zejunliu@illinois.edu
The Department of Physics offers a twosemester long sequence of graduate level
Quantum Mechanics, Physics 580 and Physics 581. Both courses are essentially
thought of as a single course,
with Physics 580 covering the basic material and Physics 581 the more
advanced topics. This is the continuation of the year long course on Quantum
Mechanics. Unfortunately I did not teach part I (Physics 580) in the Fall Semester 2022 and this may cause some problems. Nevertheless I will have to assume that you
are familiar with the standard syllabus for Physics 580 which I last taught in the Fall 2017. You can fund the syllabus for the Physics 580 course that I taught in the Fall 2017 (and pdf files of my handwritten lecture notes here .
Updated on Friday May 5, 2023
Course Plan
Time Evolution of Observables and Time Dependent perturbation Theory
Heisenberg and Schrödinger pictures. The evolution operator. Time ordered
products. Timedependent perturbation theory. Fermi's Golden Rule. Applications.
Path Integrals and Quantum Mechanics
Path integrals and the Superposition Principle. The Feynman Path Integral. Path
integrals in imaginary time and Statistical Mechanics. Calculus of path
integrals for harmonic systems. Functional determinants. The semiclassical
approximation. The double well and tunneling.
Spin
The group of rotations and its representations. Integer and half integer
representations. Rotations in spin space. Spin wave functions. Spin
Hamiltonians. SpinOrbit Interaction. Spin Precession and Spin Resonance.
Adiabatic processes and Berry phases. Coherent state path integrals and the path integral for spin
Theory of Angular Momentum and the Rotation Group in Quantum Mechanics
Addition of angular momenta. ClebschGordan coefficients. ClebschGordan methods.
Applications. Scattering of distinguishable particles with spin. Rotation and tensor operators.
The WignerEckart Theorem and applications.
Identical Particles,
MultiParticle Systems and Second Quantization
Quantum statistics and identical particles. The EPR paradox, "reality" and
Bell's inequalities. Quantum entanglement. SpinStatistics connection.
Multiparticle states. Symmetrization and antisymmetrization. Young tableaux.
Exchange interactions and spin. Scattering of identical particles. Fermions and
Bosons. Second Quantization. Construction of multiparticle states with the proper symmetry. Fock
space. Creation and annihilation operators. Normal ordering. Hamiltonians. Free
fermions and the filled Fermi sea. Interacting fermions. Multielectron atoms and simple molecules. Hartree and HartreeFock approximations. Coulomb
interactions. Quantum matter at finite density and
collapsed stars.
Interaction of Radiation with Matter
Review of Classical Electromagnetism. Vector potentials. Maxwell's Equations.
Energy and momentum of the electromagnetic field. Classical interaction of
matter with the electromagnetic field. Minimal coupling and gauge invariance.
The Schrödinger equation for matter coupled to the electromagnetic field.
Absorption and emission of light.
The Quantized Electromagnetic Field
Coulomb gauge. Transverse photons. Creation and annihilation operators. Mode
expansions. Momentum, energy and angular momentum. Interaction of
nonrelativistic particles with the quantized electromagnetic field.
Spontaneous emission. Einstein's coefficients. Electric dipole transitions.
Cross sections and Sum Rules.
Relativistic Quantum Mechanics
Quantum mechanics and Special Relativity. The KleinGordon Equation. Solutions
and particle interpretation. The KleinGordon equation and scalar field theory. The Dirac
Equation. Nonrelativistic limit. Relativistic covariance of the KleinGordon
and Dirac equations.
Particles and Antiparticles. The Dirac sea. The SpinStatistics
Theorem. The Klein paradox and pair production.
The Hydrogen atom and the Dirac equation;
bound state spectrum.
Syllabus for Quantum Mechanics I,
Physics 580, Fall Semester 2017
Grades
Please find below the HW sets. Please notice the clearly shown deadlines. There will be a total of 7 (7) homework sets.
The final set will play the role of the (take home) final exam.
The final exam will have the same
weight (1/7) as any of the other homework sets. However, since it is the Final Exam
you must take it or otherwise you will not be able to pass this class.
To upload the pdf file of your work you will go to the Physics 581 space in my.physics. There you will find the link "Course uploads" and clicking on it you will be able to upload your solutions and
download the graded solutions. There you will see a menu with the list of homeworks for Physics 581 and you will choose which homework solution you wish to upload.
Alternatively, you can go to the link
https://my.physics.illinois.edu/courses/upload/set_session.asp?s=PHYS&n=581) to access the relevant homework folder.
After the homework is graded by the TA you will be able to access and download the graded work by using this same link. The homework sets are
due on the due date posted on this webpage and have to be uploaded before midnight on that date. There will be a 20%
grade penalty on late homework sets and no homework sets will be accepted of they are
more than three days late (barring extenuating circumstances which will only be
considered by the Instructor, not by the TA.)
You may check your grades by looking at your entry in the
Physics 581 Gradebook
Homeworks
Homework Set No. 1 ;
pdf file
posted Friday January 20, 203; Due date Friday February 3, 2023, at 9:00 pm US Central Standard Time
Solutions to Homework Set No. 1
Homework Set No. 2 ; pdf file
posted Friday February 3, 2023; Due date Friday February 17, 2023, 9:00 pm US Central Standard Time
Solutions to Homework Set No. 2
Homework set No. 3 ; pdf file
posted Friday February 17, 2023; Due date Friday March 3, 2023, 9:00 pm US Central Standard Time ; deadline extended to Friday March 10, 9 pm US CST.
Solutions to Homework Set No. 3
Homework set No. 4 ; pdf file
posted Friday March 10, 2023; Due date Sunday March 26, 2023, 9:00 pm US DST
Solutions to Homework Set No. 4
Homework set No. 5 pdf file
posted Friday March 24, 2023; Due date Sunday, April 9, 2023, 9:00 pm US CDT
Solutions to Homework Set No. 5
Homework set No. 6/; pdf file
posted Monday April 10, 12 pm US CDT (edited on 4/19/23) Due date Friday April 28, 2023, 9:00 pm US CDT
Solutions to Homework Set No. 6
Homework set No. 7 / Take Home Final Exam; pdf file
posted Friday April 28, 2023; Due date: Thursday May 11, 2023, 9:00 pm US CDT
Note: This is a takehome Final Exam.
No late uploads will be accepted. Since this problem set is a take home Final Exam, you must turn in your solutions to pass this course. You must make sure that the pdf file is clearly legible!.
Please either prepare the solutions in LaTeX . If your solutions are handwritten you must write them with dark pen with clearly legible handwriting in double spaced paper. I cannot grade solutions with bad handwriting and/or with random organization. They must be clearly organized with your results shown clearly. Your solutions must be uploaded in the same manner as the HW sets.
Bibliography
Required textbooks
J. J. Sakurai, "Modern Quantum Mechanics", Revised Edition, AddisonWesley/Longman
(1994).
R. Shankar, "Principles of Quantum Mechanics", Second Edition, Plenum Press
(1994).
Recommended textbooks
L. D. Landau and E. M. Lifshitz, "Quantum Physics", Third Edition , Course of
Theoretical Physics, Volume 3. Pergamon Press (1991).
Gordon Baym, "Lectures on Quantum Mechanics", Addison Wesley (1990).
Eugene Merzbacher, "Quantum Mechanics", Second Edition, J. Wiley & Sons (1970).
Leonard Schiff, "Quantum Mechanics", Third Edition, McGrawHill (1968).
Albert Messiah, "Quantum Mechanics", Dover (1999).
Kurt Gottfried and TungMow Yan, "Quantum Mechanics: Fundamentals", 2nd.
edition, Springer
(2003).
Ernest S. Abers, "Quantum Mechanics", Pearson/ Prentice Hall (2004).
