Mathematical Methods in Quantum Mechanics

Mathematical Methods in Quantum Mechanics (Fall 2025) introduces linear algebra in the context of studying quantum physics. While the class will begin using the wavefunction ψ(x) as a starting point for describing quantum systems, we will quickly progress to thinking of quantum states in what we call “bra” 〈ψ∣ and “ket” ∣ψ〉 or “Dirac” notation. (This notation was introduced by noted physicist Paul Dirac in his 1939 publication A New Notation for Quantum Mechanics.)

We will consider questions such as:

• What do wavefunctions and Dirac notation physically represent, and why do professional physicists mainly use Dirac notation to discuss quantum systems?

• How do we move back and forth between the wavefunction and Dirac notations for a given quantum system?

• What do the eigenvalues and eigenvectors of an operator in quantum mechanics physically represent?

• What is the current state of quantum technology, and where does “the math” fit into it?

You can expect problem sets to include both analytical and computational quantum physics problems, with Python as the preferred programming language. Please note that computational problems will vary in difficulty so that all students, regardless of programming experience, will be challenged by the assignments.

Knowledge of calculus is required for this class.

This class will meet virtually on Wednesdays from 4:30 to 6:00 PM Pacific time and Thursdays from 4:30 to 6:30 PM Pacific time from September 24 to December 4, with a break the week of November 26.

Applications for Fall 2025 are due July 20th. After that, we will continue to accept applications on a rolling basis while spots remain. Click here to apply!