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PHYSICS 017
Physics 017 is a [relatively] new course at UC Riverside focusing on the mathematical framework quantum mechanics. The course is offered in Spring 2023 and will be taught by Prof. Flip Tanedo.
Course Information
Course Information
Lecture: Tue/Thu 2:00pm - 3:20pm, Winston Chung Hall Room 142 [CRN: 69513]
Discussion: Fri 1:00 - 1:50pm, Physics, Room 2111 [CRN: 69515]
Syllabus (pdf)
Vector spaces are a mathematical pillar of modern physics. The study of vector spaces is linear algebra. In this class, students will learn to use the language of linear algebra to understand the structure of relativity and quantum mechanics. Topics incldue:
Using index notation to indicate how physical quantities transform under symmetries. Rotation matrices and their complex generalizations.
The difference between space and time in special relativity. Inner products, metric spaces.
Quantum mechanics as linear algebra. Eigenvectors, eigenvalues, Hermitian and symmetric operators, diagonalizing (complex) matrices.
Spectral techniques in function space: differential equations as linear algebra, Fourier analysis, the origin of your favorite special functions in physics.
Special topics on the linear algebra of quantum computing, machine learning, or general relativity depending on the interest of the students.
This course is strongly recommended for students taking quantum mechanics (Physics 156) next year. Students will also be prepared to take Mathematical Methods of Theoretical Physics (Physics 231) next fall.
Pre-requisites: While there are no strict pre-requisites, we expect students to have:
a firm grasp of single variable calculus (Math 9).
and the first-year physics sequence (Physics 40 or 41). This is mainly to understand the physical motivation of our work.
Not having the formal preparation can be made up for with an enthusiasm to take time to dig into the material. If you have concerns about meeting the pre-requisites, please email Prof. Tanedo.
Why should I take this course? Physics 017 bridges a gap between Math 10/31/46 and the math used in quantum mechanics (Physics 156). Unlike Math 31, which focuses on engineering applications, Physics 017 focuses on complex vector spaces and advanced applications in physics.
Homework and Grades
Homework and Grades
Weekly short homework (20%): assigned Tuesday, due Thursday of the same week.
Every-two-weeks long homework (30%): assigned Tuesday of odd-numbered weeks, due on third Thursday afterward (e.g. assigned Tuesday week 1, due Thursday Week 3).
Explainer video (30%): assigned on Tuesday of odd-numbered weeks, due on third Thursday afterward (e.g. assigned Tuesday week 1, due Thursday Week 3). Videos are 5~minute pedagogical explanations of one problem from the long homework to be explained to your classmates.
Peer review (20%): assigned on Thursday of odd-numbered weeks and due in one week. You will review some of your classmates' explainer videos and provide feedback.
Textbooks and Course Material (click to expand)
Textbooks and Course Material (click to expand)
"Required" Textbooks: the following textbooks are strongly recommended. Students may use a separate reference if you prefer. These books are the closest to our goals in this course, but they will be supplemented by additional reading.
Required: A Student's Guide to Vectors and Tensors, Fleisch, Daniel. Cambridge University Press; 2012 [online though UCR library; additional resources on author's site]. Presents the picture of tensors as linear maps that transform in specific ways. What's missing: eigenvectors, determinants, complex vector spaces.
Required: Linear Algebra: Step by Step, Kuldeep Singh. Oxford University Press; 2013. Covers the standard material in a first linear algebra course in a conversational and inquisitive tone. What's missing: complex vector spaces. Unfortunately there is no digital copy available, but you are welcome to substitute in any comparable textbook.
Prof. Tanedo's course notes
2023 Course Notes (being written as we go)
2022 Course notes (hand written)
P231 Course Notes (graduate-level)
Complementary material: the following material contains chapters that help fill some of the gaps of the required textbooks relative to our course. You are not expected to purchase all of these references! Some selections will be provided during the class as appropriate for course and allowed by copyright law.
Recommended: "Physics 17" lecture notes by Flip Tanedo (Spring 2022). Hand written lecture notes from last year.
Recommended: "The Mathematics of Quantum Mechanics," Laforest; 2015. Lecture notes from the Quantum Cryptography School for Young Students. This is a fairly good summary of the material that we'll cover.
Recommended: "Physics 231" lecture notes by Flip Tanedo. The relevant sections on linear algebra and function space will serve us well. The level of the notes is a bit more advanced, but the philosophy matches our course.
Recommended: Chapter 1 ("Mathematical Introduction") of Principles of Quantum Mechanics, R. Shankar. The first chapter of this book covers all of the main ideas in our course.
Recommended: Mathematical Methods for Engineers and Scientists 1: Complex Analysis and Linear Algebra, Tang, Kwong-Tin. Springer; 2022 [online through UCR library] The second half of the book is an excellent reference for complex linear algebra. The first half of the book on complex analysis will serve you well in future graduate coursework.
Appendix ("Linear Algebra") of Introduction to Quantum Mechanics, D. Griffiths. An excellent reference on how linear algebra appears in quantum mechanics.
Optional: Linear Algebra Done Right, Axler: available free via UCR library. (2023: 4th edition now available free online.) Excellent reference for the more mathematically inclined who prefer a concise, abstract approach.
Sergei Treil's "Linear Algebra Done Wrong" is a delightful 'response' to Axler's book that is more in line with our course. It is slighlty more technically dense than our course, but otherwise covers very similar topics.
Optional: Linear Algebra, Serge Lang. This was the book from which I first learned linear algebra.
Additional chapters from: Mathematics for Quantum Mechanics, Jackson (low priced Dover edition available)
Quantum Computing for Everyone, Bernhardt (paperback now available): applications to quantum computing and an overall fun read.
A little more advanced: "Tensors: A guide for undergraduate students," American Journal of Physics 81, 498 (2013); https://doi.org/10.1119/1.4802811 (use the UCR VPN to access it)
Similarly more advanced: "Introduction to Tensor Calculus," Kees Dullemond & Kasper Peeters
For quantum computation, see Chapter 15 of the excellent textbook by Moore and Mertens, The Nature of Computation. This is the primary reference for the last 2 weeks of the course.
David Tong's introductory lectures on Quantum Mechanics, section 3 on formalism
Shankar, Basic Training in Mathematics: A Fitness Program for Science Students
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