How to use these resources
One focused problem is enough
Start with your lecture-note derivation and the precise question listed below. Open one vetted external educational source. Use the supplied investigation to calculate or reason independently, then compare it against the closest working laboratory. These extensions are optional and can be explored at any point in the course.
Using AI productively. Ask an AI tutor to guide the derivation with short hints, request a counterexample or limiting case, and challenge each assumption. Independently check equations and numerical values. Pay particular attention to basis ordering, signs in Berry phases, physical units, branch selection and the convergence of approximate methods. The original lecture notes and independently checked derivations remain the scientific reference.
Some resources link to full course chapters. Use each question to identify the relevant section. Interactive features on external sites may require a separate account.