Fall 2024: PHYS660
Tue-Thu 9:00 am – 10:15 am at Lambert Field House & Gym 105. The videos of the lectures are posted on YouTube here. The syllabus, lecture notes, and homework are posted here.
TAs are Nikhil Borse and Ibrahim Ahmed.
Course Description: In this course, we will be mostly following the structure of the textbook
“Modern Quantum Mechanics”, J.J. Sakurai
Here are some other textbooks and lectures you might find useful
“Quantum Mechanics Volume I and II” Cohen-Tannoudji, Diu, Laloe
“Quantum Mechanics” David Tong’s Lecture Notes
“Topics in Quantum Mechanics” David Tong’s Lecture Notes
MIT Open Courseware: Quantum Theory I Senthil Todadri’s Lecture Notes
MIT Open Courseware: Quantum Physics III Barton Zwiebach’s Lecture Notes
We will use the application Slack to post course announcements, and reports, discuss ideas, and share exciting papers we have come across. If you plan to attend the class please email me and I will add you to the course channel on Slack. All lectures are going to be recorded and posted on YouTube.
Homework:
The homework problems will be assigned in class and have to be submitted on Slack up to two weeks after the lecture.
Syllabus:
Click on the lecture to download the lecture notes. The syllabus is subject to change as the course progresses.
1) Quantum States, Observables and Measurement
- Lecture 1: Why QM? Two experiments
- Lecture 2: Kets, Bras and Operators
- Lecture 3: Measurements and Observables
- Problem Set 1
- Lecture 4: Incompatible observables
- Lecture 5: Uncertainty Relations and Change of Basis
- Lecture 6: Operators with Continuous Spectra
- Lecture 7: Position, Momentum and Translations
- Problem Set 2
- Lecture 8: Postulates of quantum mechanics
- Lecture 9: Density operators, pure vs mixed states
- Problem Set 3
2) Quantum Evolution
- Lecture 10: From classical dynamics to quantum dynamics
- Lecture 11: Schrodinger equation
- Lecture 12: Schrodinger versus Heisenberg picture
- Problem Set 4
- Lecture 13: Simple harmonic oscillator
- Lecture 14: Schrodinger wave-equation
- Lecture 15: WKB approximation
- Lecture 16: Propagator and path-integrals
Problem set 5
3) Composite Quantum Systems
- Lecture 17: Entanglement, Reduced density matrices, and Quantum teleportation
- Lecture 18: EPR and Bell’s theorem
- Lecture 19: Quantum Entropy; Identical Particles and symmetrization postulate
- Lecture 20: Statistics of identical particles
- Problem set 6
4) Quantum Angular Momentum
- Lecture 21: Rotations, angular momentum and spin
- Lecture 22: SO(3) and SU(2)
- Problem set 7
- Lecture 23: Eigenvalues and eigenstates of angular momentum
- Lecture 24: Orbital angular momentum
- Lecture 25: Schrodinger equation for spherically symmetric potentials
- Problem set 8
- Lecture 26: Addition of angular momenta I
- Lecture 27: Addition of angular momenta II
- Lecture 28: Schwinger’s oscillator model of angular momentum
- Problem Set 9
Nima Lashkari 