Problems by Topic
Use this page when you know the subject area. Use Problems by Method when the technique, rather than the topic, is the important part.
Topic Map
Section titled “Topic Map”| Topic | Problem Route | Representative Skills |
|---|---|---|
| Prerequisites | Self-Diagnostic Quiz and Diagnostic Checklist | linear algebra, probability, differential equations, Fourier readiness |
| Core formalism | Exercises and Problems | basis changes, Born rule, commutators, projectors, density matrices |
| Wave mechanics | Exercise Sets | normalization, boundary conditions, spectra, current |
| Canonical numerical systems | Benchmark Problems | grid normalization, convergence, current conservation |
| Perturbation theory | Anharmonic Oscillator Perturbation | matrix elements, small parameters, first-order shifts |
| Scattering | Gaussian Potential Born and WKB Barrier Tunneling | Born approximation, WKB, current, cross sections |
| Tensor products | Tensor Product Exercises | product bases, local operators, basis ordering |
| Reduced states | Partial Trace Exercises | reduced density operators, local statistics |
| Identical particles | Identical-Particle Exercises | symmetrization, antisymmetrization, exchange |
| Fock space | Fock-Space Exercises | occupations, creation and annihilation operators |
| Quantum information | Quantum Information Problem Map | qubits, channels, stabilizers, entanglement measures |
| QFT bridge | QFT Bridge Problem Map | oscillators to fields, second quantization, scattering bridges |
Topic Selection Rule
Section titled “Topic Selection Rule”If a problem names a system, begin by topic. If it asks you to “show”, “derive”, “estimate”, “diagonalize”, “trace out”, or “check convergence”, begin by method. Many mature problems appear in both routes.
Common Topic Mismatches
Section titled “Common Topic Mismatches”- Treating a density-matrix problem as a state-vector problem because the Hilbert space is two-dimensional.
- Treating a scattering problem as a bound-state normalization problem.
- Treating an identical-particle problem as an ordinary distinguishable tensor product.
- Treating a numerical benchmark as a plotting task rather than a convergence problem.
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.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.