PHYSICS 017
Linear Algebra for Quantum

Course Information

• Lecture: (please refer to the course agenda for changes)
  Tue/Thu 2:00pm - 3:20pm, MS&E 011 [CRN: 69513]

• We will occasionally use the discussion sections, please refer to our Agenda page.
  Fri 1:00 - 1:50pm, Olmsted 1132
  (Some students say Olmstead hall is haunted.)

• Office Hours: by appointment (please ask your physics questions in class!)

• TA Office Hours: TBA

• Syllabus (pdf, updated 31 March) | Canvas Page (not used)

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

• 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.