Computational QM References
Computational quantum mechanics is where analytic formulas become algorithms with discretization errors, stability limits, basis truncations, and reproducibility requirements. A computational reference should be chosen for the numerical task, not only for the physics topic.
Use this page with the Computational Quantum Mechanics Roadmap, Computational Many-Body Overview, and the benchmark-problem guide. The software and notebook index records package documentation, validation tests, environments, and reproducible benchmark expectations.
General Computational Physics
Section titled “General Computational Physics”Thijssen, Computational Physics.
Best for: numerical methods across quantum mechanics, electronic structure, Monte Carlo, and computational physics practice.
Watch for: implementations and software ecosystems evolve; use it for methods, not current package APIs.
Landau, Páez, and Bordeianu, Computational Physics.
Best for: broad computational physics exercises, simulations, and numerical experimentation.
Watch for: examples are pedagogical; production research code needs stronger verification and testing.
Newman, Computational Physics.
Best for: accessible numerical methods, Python-oriented examples, and general scientific computing habits.
Watch for: it is not specialized to quantum mechanics, so pair it with quantum-specific references.
Quantum Dynamics and Propagation
Section titled “Quantum Dynamics and Propagation”Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective.
Best for: time-dependent propagation, wave packets, control, and physical interpretation of quantum dynamics algorithms.
Watch for: numerical recipes should be validated against analytic benchmark problems.
Feit, Fleck, and Steiger, split-operator spectral method paper.
Best for: Fourier split-operator propagation and spectral treatment of time-dependent Schrödinger equations.
Watch for: periodic grids, aliasing, and boundary handling are numerical assumptions, not physical boundary conditions by default.
Kosloff, time-dependent quantum-mechanical methods review.
Best for: wave-packet propagation, pseudospectral methods, and molecular dynamics applications.
Watch for: numerical method names can vary across communities; identify the algorithm precisely.
Linear Algebra and Eigenproblems
Section titled “Linear Algebra and Eigenproblems”Golub and Van Loan, Matrix Computations.
Best for: dense and structured numerical linear algebra, conditioning, decompositions, and stability.
Watch for: it is method-focused; the quantum interpretation must come from physics sources.
Saad, Numerical Methods for Large Eigenvalue Problems.
Best for: Krylov methods, sparse eigenvalue problems, Lanczos and Arnoldi algorithms.
Watch for: convergence diagnostics and reorthogonalization are part of the method, not optional implementation details.
Trefethen and Bau, Numerical Linear Algebra.
Best for: conceptual clarity about stability, conditioning, orthogonality, and matrix algorithms.
Watch for: it is not quantum-specific but prevents many numerical mistakes in diagonalization workflows.
Open Systems and Packages
Section titled “Open Systems and Packages”Johansson, Nation, and Nori, QuTiP papers.
Best for: citing QuTiP as a package framework for open quantum systems, quantum optics, and driven dynamics.
Watch for: cite the package documentation and version for reproducible code, not only the original papers.
Breuer and Petruccione, The Theory of Open Quantum Systems.
Best for: master equations, Markov approximations, open-system derivations, and physical assumptions behind simulations.
Watch for: numerical use requires method-specific validation beyond the formal master equation.
Reproducibility Checks
Section titled “Reproducibility Checks”- State the basis, grid, truncation, and boundary conditions.
- Benchmark against analytic spectra or conserved quantities when possible.
- Distinguish physical error from discretization error.
- Record package versions and random seeds when results depend on them.
- Use dimensionless units deliberately, and document how physical units are restored.
Cross-Links
Section titled “Cross-Links”- Computational Quantum Mechanics Roadmap
- Exact Diagonalization Preview
- Benchmark Problems
- Harmonic Oscillator Spectrum
- Density Matrix Convention Translator
References
Section titled “References”- J. M. Thijssen, Computational Physics, 2nd ed., Cambridge University Press, 2007.
- R. H. Landau, M. J. Páez, and C. C. Bordeianu, Computational Physics: Problem Solving with Python, 3rd ed., Wiley-VCH, 2015.
- M. E. J. Newman, Computational Physics, CreateSpace, 2012.
- D. J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective, University Science Books, 2007.
- M. D. Feit, J. A. Fleck Jr., and A. Steiger, “Solution of the Schrödinger equation by a spectral method,” Journal of Computational Physics 47, 412-433 (1982), DOI: 10.1016/0021-9991(82)90091-2.
- R. Kosloff, “Time-dependent quantum-mechanical methods for molecular dynamics,” Journal of Physical Chemistry 92, 2087-2100 (1988), DOI: 10.1021/j100319a003.
- G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed., Johns Hopkins University Press, 2013.
- Y. Saad, Numerical Methods for Large Eigenvalue Problems, 2nd ed., SIAM, 2011.
- L. N. Trefethen and D. Bau III, Numerical Linear Algebra, SIAM, 1997.
- J. R. Johansson, P. D. Nation, and F. Nori, “QuTiP: An open-source Python framework for the dynamics of open quantum systems,” Computer Physics Communications 183, 1760-1772 (2012), DOI: 10.1016/j.cpc.2012.02.021.
- J. R. Johansson, P. D. Nation, and F. Nori, “QuTiP 2: A Python framework for the dynamics of open quantum systems,” Computer Physics Communications 184, 1234-1240 (2013), DOI: 10.1016/j.cpc.2012.11.019.
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, 2002.