Problem Index
The problem index turns the reference layer into a curriculum map. It indexes problems by what they teach: normalization, basis changes, boundary conditions, perturbative estimates, scattering checks, tensor-product bookkeeping, density matrices, and bridge skills.
This page does not replace problem sets on teaching pages. Use it to choose a problem route, then follow the canonical link for the actual solution, hint, or exercise set.
Main Routes
Section titled “Main Routes”- By Topic
- By Level
- By Method
- Diagnostic Problems
- Undergraduate Problem Map
- Graduate Problem Map
- Quantum Information Problem Map
- QFT Bridge Problem Map
Problem Record Format
Section titled “Problem Record Format”Each problem route should be describable with a stable record:
| Field | Meaning |
|---|---|
| Problem ID | Stable identifier such as QM-PROB-0101 |
| Level | Orientation, undergraduate, advanced undergraduate, graduate bridge, or research style |
| Skills | The operations being practiced |
| Prerequisites | Mathematical and physical pages to review first |
| Solution status | Unsolved, hint, short solution, full solution, notebook, or benchmark |
| Canonical page | The page that owns the problem or solution |
Index pages should not reveal full solutions unless the page is explicitly diagnostic. They should make the path clear and preserve the canonical-home rule.
Launch Problems
Section titled “Launch Problems”| ID | Problem Family | Canonical Page | Solution Status |
|---|---|---|---|
| QM-PROB-0101 | Prerequisite self-check | Self-Diagnostic Quiz | full solution |
| QM-PROB-0201 | Formalism calculations | Exercises and Problems | full solution |
| QM-PROB-0301 | Wave-mechanics exercise sets | Exercise Sets | mixed solution status |
| QM-PROB-0302 | Numerical wave-mechanics benchmarks | Benchmark Problems | benchmark criteria |
| QM-PROB-0401 | Approximation worked problems | Anharmonic Oscillator Perturbation | worked problem |
| QM-PROB-0402 | Scattering worked problems | Gaussian Potential Born | worked problem |
| QM-PROB-0501 | Tensor-product exercises | Tensor Product Exercises | full solution |
| QM-PROB-0502 | Partial-trace exercises | Partial Trace Exercises | full solution |
| QM-PROB-0601 | QFT bridge route | QFT Bridge Problem Map | route map |
How to Use This Index
Section titled “How to Use This Index”- Pick the topic or method that blocks you.
- Check the prerequisite links before attempting the problem.
- Work without the solution first.
- Compare your answer with the canonical solution or benchmark criteria.
- Record the error type: convention, algebra, interpretation, approximation, or missing prerequisite.
The most useful problem is often the one that diagnoses a weak assumption, not the one that looks most advanced.
References
Section titled “References”- D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
- R. Shankar, Principles of Quantum Mechanics, 2nd ed., Springer, 1994.
- J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.
Exercises
Section titled “Exercises”- A reader can compute eigenvalues but keeps missing probabilities after a measurement. Which route should they use first?
Solution
Use Problems by Method and start with Born-rule and basis-change problems in Exercises and Problems. The obstacle is converting states into measurement probabilities, not diagonalization by itself.