Bound States and Spectra
Compare exact spectra with variational, grid and self-consistent calculations. Keep the physical model, basis truncation and numerical error distinct.
Choose an investigation
Section titled “Choose an investigation”- Harmonic Oscillator Spectrum — Diagonalize a grid oscillator, recover its low-lying spectrum and parity, and separate grid error from the finite-domain approximation.
- Variational Optimization Notebook — A reproducible Rayleigh-Ritz study of nonlinear basis optimization, energy landscapes, convergence, virial stationarity, and numerical failure modes.
- Double-Well Instanton Numerical Check — A reproducible parity-resolved comparison of exact double-well splittings with finite-energy WKB and one-loop instanton estimates.
- Variational Helium Notebook — A reproducible effective-charge calculation for helium with analytic and numerical optimization, unit checks, variational and virial validation, and an explicit correlation-deficit ledger.
- Hartree–Fock Notebook — A reproducible closed-shell helium calculation with analytic Gaussian integrals, Roothaan equations, self-consistent density iteration, convergence studies, and orbital-energy caveats.
- Molecular Orbital Computation — A reproducible minimal-LCAO calculation for the hydrogen molecular ion with overlap matrices, generalized diagonalization, bonding and antibonding curves, axial densities, and validation tests.
- Vibrational Spectra Computation — A reproducible normal-mode and anharmonic-spectrum calculation with a calibrated CO₂ Hessian, an H³⁵Cl Morse sinc-DVR benchmark, transition moments, convergence tests, and experiment-facing error analysis.
Interpret the evidence
Section titled “Interpret the evidence”The Labs catalog distinguishes downloadable pilot packages from other existing script-backed investigations. Each investigation states its own assumptions and retained checks. Follow Running an Experiment for the shared execution workflow and the Reproducibility Checklist for evidence and error budgets.
References
Section titled “References”- National Academies of Sciences, Engineering, and Medicine, Reproducibility and Replicability in Science, National Academies Press, 2019, doi:10.17226/25303 — interpreting reproducibility and independent scientific evidence.