Direct Method: Guided Research in Quantum Mechanics and Spectroscopy

Disclaimer. This course is under active development. Some chapters, examples, or links may contain mistakes or may change as the notes are revised.

What this is

A route into research for an undergraduate, run one student at a time rather than as a class. The physics is quantum mechanics and spectroscopy, and the notes cover it properly — from the postulates through angular momentum, perturbation theory and time dependence, and on to what a spectrum actually measures and how to compute one well enough to compare against a real measurement.

But the notes are the means, not the end. What a student is here to learn is how research works: how to take a question that has no answer in the back of the book, decide what would count as an answer, build something that produces one, and then find out whether to believe it.

How it runs

The shape follows the student. The usual arrangement is a weekly meeting, a problem set per chapter to keep the physics moving, and a final report written to the format on the projects page — a piece of work that stands on its own outside the course, and that a student can show to a graduate programme.

The computational half is not a track bolted on at the end. Where a result can be obtained numerically it is, in code the student writes and runs themselves. Running someone else's program teaches nothing that lasts.

Who it suits

An undergraduate who has met quantum mechanics once and wants to use it, and who can already program well enough to write a numerical integrator without help. Mathematical Methods, or the equivalent, covers the mathematics this leans on.

You do not need to have finished the whole quantum sequence, and you do not need to know what you want to work on yet. Curiosity and persistence matter more here than coverage — see joining the group.