Physics 342: Quantum Mechanics I

This course is an introduction to the microscopic physical description of the natural world. Quantum mechanics is an entirely novel framework in which to view the world in contrast to classical mechanics, and this class introduces formalism, principles, and examples which underly almost all of contemporary physics and much of modern technology.

The course materials are provided below. The textbook for the class will primarily be my lecture notes and a recommended text is David Griffiths & Darrell Schroeter's book "Introduction to Quantum Mechanics," 3rd Edition, Cambridge University Press, 2018.

Course Syllabus

Oral Exam

I have decided that the oral exam is impractical given the online structure of the course now. There will be no oral exam component of this class.

Final Project

There will be a final project for this course. You will be required to write a 3-5ish page review paper on a topic of choice related to quantum mechanics. Please write the paper in Physical Review, two-column format that you are familiar with from laboratory courses. (Contact me directly if this is unfamiliar to you.) A very incomplete list of potential topics is presented at the bottom of this page, but you are welcome to come up with your own project idea. Please contact me with your idea for a project topic first, as every student must have a unique topic. This review paper is required to have at least three unique references from the physics literature (i.e., not Wikipedia articles). More information will be provided throughout the rest of the semester, and please contact me if you have any questions.
You can find the RevTeX template, installation instructions, and more information here.
The paper is due on Tuesday, May 12.

Lecture Notes

1. Introduction and Overview
2. Linear Operators
3. Eigenvalues
4. Momentum
5. Hilbert Space
6. Hermitian Operators
7. Dirac Notation
8. Hamiltonian
9. Born Rule
                Reading for Week 4: Chapter 1 in Griffiths and Schroeter
10. The Schrodinger Equation Video of Lecture
11. Ehrenfest's Theorem Video of Lecture
12. Heisenberg Uncertainty Principle Video of Lecture
                Reading for Week 5: Sections 2.1, 2.2 in Griffiths and Schroeter
13. Infinite Square Well
14. Correspondence Principle
15. Intro to the Density Matrix
                Reading for Week 6: Section 2.3 in Griffiths and Schroeter
16. Harmonic Oscillator
17. Energy Eigenstates of the Harmonic Oscillator
18. Coherent States
                Reading for Week 7: Sections 2.4-2.6 in Griffiths and Schroeter
19. Free Particle
20. Scattering Theory
21. The S-matrix
22. Rotations in Two Dimensions
23. Rotations in Three Dimensions
24. Lie Algebra for Rotations
25. Representations of Rotations
26. Casimir of Rotations
27. Quantum Numbers
                Reading for Week 10: Chapter 4 in Griffiths and Schroeter
28. The Hydrogen Atom
29. Energy Levels of Hydrogen
30. Spherical Harmonics
                Reading for Week 11: Section 7.1 and Chapter 8 in Griffiths and Schroeter
31. Quantum Perturbation Theory
32. The Variational Method
33. The Power Method
34. Derivation of the Path Integral: Part 1
35. Derivation of the Path Integral: Part 2
36. Derivation of the Schrodinger Equation from the Path Integral
37. The Density Matrix
38. Entropy
39. Thermal Equilibrium and the Imaginary Path Integral

Homework Assignments

Homework 1 Due February 7
                Solutions
Homework 2 Due February 14
                Solutions
Homework 3 Due February 21
                Solutions
Homework 4 Due February 28
                Solutions
Homework 5 Due March 6
                Solutions
Homework 6 Due March 13
                Solutions
Homework 7 Due March 30
                Solutions
Homework 8 Due April 3
                Solutions
Homework 9 Due April 10
                Solutions
Homework 10 Due April 17
                Solutions
Homework 11 Due April 24
                Solutions

Example Final Project Topics and where to find references

Reference Searching Online:
The Preprint arXiv
InSpire
Astrophysics Data System

(1) Neutron Stars
(2) Lasers
(3) The Standard Model
(4) Quantum Computing
(5) Entanglement
(6) Bell's Inequalities
(7) Decoherence
(8) The Ising Model
(9) Bose-Einstein Condensates
(10) Superconductivity
(11) Hawking Radiation
(12) Josephson Junctions
(13) Quantum Hall Effect
(14) Anomalous Magnetic Moment of the Electron
(15) Superfluidity
(16) Interpretations of Quantum Mechanics
(17) Phase Transitions
(18) The Planck Scale
(19) Neutrino Oscillations
(20) Supersymmetry
(21) Wigner's Theorem
(22) The Dirac Equation
(23) Wigner Function/Distribution