Labs
Explore quantum mechanics through executable investigations. Each lab connects a physical question to its model, implementation, numerical checks and limitations. Use the subject Library for the underlying derivations and Computational Quantum Mechanics for general numerical methods.
Start with a complete experiment
Section titled “Start with a complete experiment”These three packages include their required source, a single entry command, the tested environment specification, and scientific acceptance checks. Their linked verification records describe an actual execution of the downloadable package.
| Experiment | Investigate | Main checks |
|---|---|---|
| Harmonic Oscillator Spectrum | How well does a grid recover the whole-line spectrum? | Exact energies, parity, normalization, residuals, mesh and boundary refinement |
| Landau–Zener Transition | Is a discrepancy caused by finite sweep duration or the integrator? | Independent propagators, convergence order, norm and endpoint studies |
| Dirac Wave Packets | How do energy sectors and coherence affect a relativistic packet? | Projectors, currents, propagation, refinement and position diagnostics |
Begin with Running an Experiment. A successful execution is useful evidence, but the physical model and numerical acceptance criteria determine what a result establishes.
Browse by physical question
Section titled “Browse by physical question”Compare exact spectra with variational, grid and self-consistent calculations. Keep the physical model, basis truncation and numerical error distinct.
Harmonic Oscillator Spectrum · Variational Optimization · Double-Well Instanton Numerical Check · Variational Helium · Hartree–Fock · Molecular Orbital Computation · Vibrational Spectra Computation
Follow coherent transitions, dissipative evolution and control protocols. Norm conservation, complete positivity where applicable, and step refinement answer different questions.
Landau–Zener Simulation · Magnus Expansion Error · Time-Dependent Two-Level Systems · Optical Bloch Equation · Cavity QED Simulation · Laser Cooling Simulation
Relate numerical wave packets and amplitudes to the incident-flux and asymptotic conventions used by scattering theory.
Wave-Packet Scattering · Born Approximation Numerical Test
Investigate relativistic wave equations, energy sectors, current and controlled nonrelativistic limits. One-particle wave mixing does not by itself measure field-theoretic particle creation.
Lorentz Transformations · Klein–Gordon Wave Packets · Dirac Wave Packets · Spinor Algebra · Foldy–Wouthuysen Expansion · Relativistic Landau Levels · Klein Paradox · Mott Scattering · Propagator Visualization
Shared guides
Section titled “Shared guides”What belongs in Labs
Section titled “What belongs in Labs”The collection currently contains 24 computational investigations. The three introductory packages have a common executable entry point and source-bound verification reports. Other investigations retain their own scripts, data, run instructions and evidence; their inclusion here does not imply a new execution or a blanket verification claim. Shared workflow guides, plotting helpers and datasets are not additional labs.
A lab owns a specific investigation. Its underlying theory remains at the linked subject page, and a code snippet that directly supports a theoretical argument may remain there. General numerical analysis belongs in Computational Quantum Mechanics.
References
Section titled “References”- National Academies of Sciences, Engineering, and Medicine, Reproducibility and Replicability in Science, National Academies Press, 2019, doi:10.17226/25303 — reproducibility, replicability and the limits of execution evidence.