PHYSICS 017
Linear Algebra for Quantum

Course Information

• Tue/Thu 12:30pm - 1:50pm, Physics 2104

• Course Canvas Page (for additional readings)

• Refer to the Agenda for assignments and course notes

• Office hours:

  • Ian: Wed 1:30pm, Monday 2pm (PHYS 3028)

  • Prof. Tanedo: by appointment

The goal of this course is to develop the mathematical tools to study quantum mechanics (Physics 156). The target audience are students who will be taking quantum mechanics the following fall quarter; it should also be of interest to advanced freshmen or curious students from other departments. The main topic is linear algebra with a dose of complex variables and basic differential equations. Our main application of these ideas will be a basic understanding of quantum computing.

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.

• You should have an idea of matrix multiplication from pre-calculus, at the level of this example from Khan Academy.

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. 

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.

Textbook(s):

• 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. Selections available on our Canvas page.

• Appendix ("Linear Algebra") of Introduction to Quantum Mechanics, D. Griffiths. Selections available on our Canvas page.

• Optional: Linear Algebra Done Right, Axler: available free via UCR library

• Optional: Linear Algebra, Serge Lang

• Optional (recommended): Introduction to Quantum Mechanics, David Griffiths. The appendix on linear algebra is a great reference.

• Additional chapters from: Mathematics for Quantum Mechanics, Jackson (low priced Dover edition available)

• Additional notes: "The Mathematics of Quantum Mechanics," Laforest; this is a fairly good summary of the material that we'll cover.

• 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.