## 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.

**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