quantum-mechanics

name	quantum-mechanics
description	Formulate, solve, simulate, and verify nonrelativistic quantum mechanics problems using states, operators, boundary conditions, symmetries, stationary and time-dependent evolution, approximation methods, measurement, and open-system dynamics.
license	MIT

Quantum Mechanics

Define the quantum model

1. State Hilbert space, degrees of freedom, Hamiltonian, domain and boundary conditions, units, initial state or density operator, observables, and requested probabilities or expectation values.
2. Declare approximations: nonrelativistic, single-particle, Born-Oppenheimer, spinless, finite basis, rotating-wave, Markovian, or other truncations.
3. Check that operators have appropriate domains and that claimed observables are Hermitian/self-adjoint under the chosen boundary conditions.
4. Nondimensionalize or choose natural units explicitly; never silently set constants to one.

Choose a route

• Stationary states: solve the spectral problem and enforce normalizability and boundary conditions.
• Time evolution: use unitary propagation for closed systems and a declared master equation for open systems.
• Symmetry: identify commuting operators, conserved quantities, degeneracy, and compatible quantum numbers.
• Approximation: use perturbation, variational, semiclassical, adiabatic, or finite-basis methods only with a stated small parameter or variational space.
• Few-level/open systems: load kdense-qutip for computation, while retaining this physics validation contract.

Compute

1. Normalize states and keep global phase distinct from relative phase.
2. Preserve complex conjugation, operator order, and tensor-product structure.
3. Resolve degeneracy before applying nondegenerate perturbation formulas.
4. Demonstrate basis and cutoff convergence for discretized or truncated calculations.
5. For measurement, distinguish amplitudes, probabilities, expectation values, and post-measurement states.

Verify

• Check normalization, positivity and unit trace of density operators, and probability bounds.
• Check Hermiticity, commutators, orthogonality, completeness within the retained space, and units.
• For closed evolution, check norm/energy conservation and unitarity; for open evolution, check trace preservation and complete-positivity assumptions of the generator.
• Substitute eigenfunctions into the operator and boundary conditions.
• Test free-particle, zero-coupling, classical/semiclassical, symmetry, and short-time limits.
• Compare analytic and numerical spectra and show grid/basis/time-step convergence.

Deliver

Report model and approximations, state/operator definitions, result, probabilities or observables, convergence checks, and physical interpretation. Do not treat an unnormalized wavefunction or an arbitrary finite-basis eigenpair as a physical prediction.

Source basis

This workflow is independently synthesized from Crowell's openly licensed Modern Physics and the existing QuTiP workflow; source provenance is recorded in ../../docs/TEXTBOOK_SOURCES.md.