Syllabus of Quantum Mechanics II (PHYS 482/682)
In the early 20th century, there were several critical discrepancies between experiments and classical theories, such as the famous ultraviolet catastrophe. New theory, instead of patches of classical theories, was required. Pioneered by a group of genius scientists, such as Bohr, Plank, Schrodinger, Heisenberg, Einstein, Dirac, etc., quantum mechanics was developed. Quantum mechanics not only fixed the discrepancies, but also successfully predicted new experimental phenomena. Since then, new science and technologies based on quantum mechanics have changed people's life substantially in the past fifty years.
PHYS 482/682 is the second semester course of introduction level quantum mechanics. I assume the students have already know how to solve Schrodinger equations with simple 1D potentials, mastered Dirac notations and matrix formalism, and understood quantum mechanical description of hydrogen atom, including angular momentum and spin. In this class, I will spend one third semester introducing more fundamental quantum mechanics concepts, such as quantum statistics of few-body system, angular momentum coupling and symmetries. Then, I will use the second one third semester to introduce the most important approximation method - perturbation theory and its applications. Last, I will briefly introduce some relatively advanced topics, such as quantum chemistry calculation, scattering theory, quantum dynamics and quantum information processing. After this class, the students are expected to master enough knowledge to conduct experimental research or industrial jobs using basic quantum mechanics or are ready for further advanced 700-level quantum mechanical classes.
PHYS 482/682 is a hybrid course with mixed senior undergraduate students (PHYS 482) and junior graduate students (PHYS 682). The lectures are the same for the two groups of students. Additional problems in homework and tests might be added for graduate students.
Textbook
Introduction to Quantum Mechanics, Third Edition. Authors: David J. Griffiths, Darrell F. Schroeter. Publisher: Cambridge University Press; 3 edition (August 16, 2018). ISBN-10: 1107189632. ISBN-13: 978-1107189638.
Grade Criterion
1. Eight problem sets (40 pts)
2. Two tests (30 pts for each)
Prerequisite requirements
1. Calculus
2. Linear algebra
3. Complex number
4. Classical mechanics
5. Electrodynamics
6. Programming
7. Quantum Mechanics I
Lecture Videos
Course outline
- Identical particles (week 1-3)
- Review angular momentum and spin
- Angular momentum addition
- Two-particle system – basic quantum statistics
- Perturbation theory (week 4-6)
- Non-degenerate perturbation theory
- Degenerate perturbation theory
- Variational principle
- Mid-term exam (week 8)
- Application of perturbation theory (week 7-9)
- Fine structures of Hydrogen
- Hyperfine structures of Hydrogen
- Electric and magnetic fields
- Hydrogen molecular ion
- Quantum dynamics (week 10-12)
- Time-dependent perturbation theory
- Three pictures of quantum dyanmics
- Atom-photon interactions
- Adiabatic processes
- Special topic: quantum information processing
- Special topics (week 13-14)
- WKB approximation
- Scattering
- Final exam (week 15)