Physics / advanced
Numerically evolve and interrogate quantum systems
Compute quantum spectra and dynamics while controlling normalization, unitary error, boundary artifacts, Hilbert-space truncation, and physical interpretation.
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Inside this module
Module 01 advanced
Numerically evolve and interrogate quantum systems
Compute quantum spectra and dynamics while controlling normalization, unitary error, boundary artifacts, Hilbert-space truncation, and physical interpretation.
- 01
Discretizing Schrödinger operators and boundaries
Construct a finite Hamiltonian while keeping normalization, boundary conditions and dispersion errors explicit.
30 min - 02
Shooting and matching for bound eigenstates
Turn endpoint consistency into an energy root and distinguish genuine matching from numerical contamination.
30 min - 03
Split-operator Fourier time evolution
Fix FFT signs and periodic modes before composing kinetic and potential propagators.
30 min - 04
Crank–Nicolson unitarity and solver tolerance
Analyze a unitary rational propagator and the errors introduced by phase distortion and incomplete linear solves.
30 min - 05
Absorbing boundaries and reflection artifacts
Interpret controlled norm loss, artificial reflection and finite-domain sensitivity without inventing a physical detector.
30 min - 06
Quantum wavepacket scattering numerics
Connect incident spectra, asymptotic flux ratios and discrete probability currents in finite-domain calculations.
30 min - 07
Time-dependent basis truncation and convergence
Control representation error with moving-basis connections, state residuals and bounded propagator approximations.
30 min - 08
Numerical Lindblad evolution and positivity
Distinguish a physical finite master equation from a numerical update that only preserves trace.
30 min - 09
Quantum-trajectory Monte Carlo estimators
Connect stochastic pure-state paths to density matrices while separating sampling noise from propagation bias.
30 min - 10
Benchmarking quantum dynamics against exact models
Use independent exact solutions and nested convergence studies to identify coherent, numerical and modeling errors.
30 min