Problems by Level
Levels describe assumed independence, not intellectual value. A graduate calculation can fail because of a first-course normalization convention, so use the lowest level that diagnoses the real obstacle.
Level Map
Section titled “Level Map”| Level | Route | Expected Output |
|---|---|---|
| Orientation | Self-Diagnostic Quiz and Diagnostic Problems | identify missing prerequisites |
| Undergraduate | Undergraduate Problem Map | solve standard formalism and wave-mechanics problems with checks |
| Advanced undergraduate | Exercise Sets and Tensor Product Exercises | combine exact models, spin, approximation, and composite systems |
| Graduate bridge | Graduate Problem Map | state assumptions, domains, degeneracies, and approximation limits |
| Quantum information bridge | Quantum Information Problem Map | use density matrices, channels, and entanglement measures |
| QFT bridge | QFT Bridge Problem Map | connect oscillator, Fock-space, path-integral, and scattering language |
| Computational | Benchmark Problems and Numerical Benchmark Problems | convergence evidence and benchmark pass criteria |
Level-Up Criteria
Section titled “Level-Up Criteria”Move up a level when you can do the following without copying a template:
- state the Hilbert space and basis;
- identify the Hamiltonian and observable;
- normalize or explain the normalization convention;
- compute probabilities or expectation values;
- check dimensions and limits;
- explain whether the result is exact, approximate, numerical, or conceptual.
Solution Status Guide
Section titled “Solution Status Guide”| Status | Use |
|---|---|
unsolved_exercise |
Practice without assistance |
hint_available |
Use when stuck on setup |
short_solution_available |
Check the result without full derivation |
full_solution_available |
Study after a serious attempt |
notebook_available |
Reproduce and vary parameters |
challenge_problem |
Expect synthesis across pages |
research_style_problem |
Expect assumptions and scope to matter more than a closed-form answer |
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.