Office Hours: Monday 12:30-1:30 Room 30
Office Hours: TBA
General Information
Syllabus
Lecture Schedule
Problem Sets
Grading:
Problem Sets: 34%
Problem sets will be distributed approimately once a week and due on Tuesdays, to be placed in the grader's mailbox by 5:00 PM.
Two Exams 66%
"Recommended" Texts:
We will not be following any text directly. Copies of my lecture note will be available. The are many good texts out there; you should pick the one(s) that work best for you. Relevant material from the following recommended texts with be referenced throughout the course.
o Modern Quantum Mechanics, by J. J. Sakurai
Good advanced text with a modern perspective. It's somewhat terse, are there are few examples.
o Quantum Mechanics , vol. II, by C. Cohen-Tannoudji, B. Diu, and F. Laloë.
Vol II of this text is not quite as good vol. I. It is a bit elementary for this course, but has some very good material, especially on atomic physics.
o Quantum Mechanics 3rd Edition, by E. Merzbacher
Everything is here but the organization is difficult. This edition and contains many contemporary topics.
Other texts:
o Quantum Mechanics, by L. I. Schiff
The old advanced classic. Still a good reference. Somewhat old fashion
o Quantum Mechanics, vol. I and II, by A. Messiah
Another older classic and good reference
Quantum Mechanics , vol. I, by K. Gottfried.
Recently republished. Contains a reasonable coverage of measurements theory.
I. Intro to Structure of Matter (5 weeks)
A. From one to multiple degrees of freedom
B. Intro to Angular Momentum in Quantum Mechanics
C. Central potentials and 3D wave mechanics
D. Nonrelativistic Hydrogen Atom
II. Time-Independent Perturbation Theory (4 weeks)
A. Nondegenerate theory - examples from atomic/molecular spectra.
B. Degenerate theory - examples: quadratic stark effect, band structure in solids, relation to symmetries.
III. Time-Dependent Perturbations (2 weeks)
A. Transition Probabilities
B. Coherent Rabi Flopping
C. Fermi's Golden rule
IV. Symmetries and Groups (5 weeks)
A. Symmetries and group theory in quantum mechanics.
B. SU(2) and irreducible representations.
C. General theory of addition of angular momentum.
D. Tensor operators, Wigner-Eckart theorem, multipole selection rules.
E. Identical particles, spin, and permutation symmetry - application to multielectron atoms.
Tentative Schedule of Lectures
Date
Topic
Downloads
Review of Quantum I
Basic Structure of Quantum Mechanics
Lecture 1
Podcast 1
From Hilbert Space to Physical Space
Lecture 2
Podcast 2
Multiple Degrees of Freedom
Lecture 3
Podcast 3
Jan. 28
Continuation -- Separability
Podcast 4
Symmetries and Degeneracy
Lecture 4
Podcast 5
Continuation -- Complete Sets and Integrabilty
Supplement
Podcast 6
Feb. 9
Rotations and angular momentum algebra
Eigenvalue problem for angular momentum
Lecture 5
Lecture 6
Podcast 7
Feb. 11
Oribtal angular momentum and spherical harmonics
Lecture 7
Podcast 8
Feb. 16
Central Potentials
Free particle in Spherical Coordinates
Lecture 8
Podcast 9
Feb. 17
Partial Waves and Spherica Wells
Lecture 9a
Lecture 9b
Podcast 10
Lecture 10a
Podcast 11
Lecture 10b
Podcast 12
Time independent nondegenerate perturbation theory (TINPT)
Lecture 11
Podcast 13
Applications of TINPT
Anharmonic Trapping. Quadratic Stark effect.
Lecture 12
Podcast 14
Time independent degenerate perturbation theory (TIDPT)
Linear Stark effect.
Lecture 13
Podcast 15
Exam
Spring Break
Avoided Crossings
Lecture 14
Podcast 16
Addition of angular momentum -- elementary theory
Lecture 15
Podcast 17
Application of TDPT:
Relativitistic effects - Fine Structure in Hydrogen
Lecture 16
Podcast 18
Application of TIDPT:
Hyperfine Structure in Hydrogen
Lecture 17
Podcast 19
Introduction to tensors
Rotation Group: SO(3) vs. SU(2)
Lecture 18
Podcast 20
Addition of Angular Momentum -- Clebsch-Gordan Coefficients
Reducible and Irreducible representations of SU(2)
Lecture 19
Podcast 21
Tensors, Irreducible Tensors, and the Spherical Basis
Lecture 20
Podcast 22
The Wigner-Eckart Theorem
Lecture 21
Podcast 23
Application -- Multipole selection rules
Lecture 22
Podcast 24
Continuation
Podcast 25
Introduction to time-dependent perturbation :
Magnetic resonance and Rabi Flopping
Lecture 23
Podcast 26
Time-Dependent Perturbation Theory
Formalism: Interaction picture and the Dysan Series
Lecture 24
Podcast 27
Transition Probabilities:
Absorption and Emission. Resonance. Time-energy uncertainty
Lecture 25
Podcast 28
Incoherent evolution: Fermi's Golden Rule
Lecture 26
Podcast 29
Continuation: Absorption rates, stimulate and spontaneous emission
Podcast 30
Problem Set #1
Due Jan. 26
Problem Set #7
Due Mar. 24
Problem Set #2
Due Feb. 2
Problem Set #8
Due Mar. 31
Problem Set #3
Due Feb. 11
Problem Set #9
Due Apr. 7
Problem Set #4
Due Feb. 18
Problem Set #10
Due Apr. 14
Problem Set #5
Due Feb. 25
Problem Set #11
Due Apr. 21
Problem Set #6
Due Mar. 3
Problem Set #12
Due Apr. 28
Problem Set #13
EXTRA CREDIT Due May 10