DeepDynaSim collection | Computational physics | Educational simulations
Visualize numerical wave-packet evolution and interactions with potential barriers. The examples are motivated by quantum mechanics and pilot-wave discussions and use MATLAB to explore wave behaviour.
| File | Focus |
|---|---|
| schrodingerequation_numerical.m | Numerical two-dimensional time-dependent Schrodinger evolution |
| potentialbarriers.m | Potential-barrier example |
| gaussianwaveinteractingpotentialbarrier.m | Gaussian wave packet interacting with a barrier |
Clone the repository, open its root folder in MATLAB and inspect the grid, time step, potential and initial wave packet in the selected script.
edit schrodingerequation_numerical.mThese scripts numerically evolve wavefunctions. Check spatial/time convergence, normalization and boundary effects when interpreting a visualization. The detailed notes below explain the included examples and retain the existing figures.
The free-particle example uses central spatial differences and circshift to wrap the grid periodically. Its time update is explicit forward Euler:
psi_next = psi - i * dt * H(psi) / hbar
It is not a Crank-Nicolson solve. For a Hamiltonian eigenmode with real eigenvalue lambda, the amplification factor satisfies
abs(1 - i*dt*lambda/hbar)^2 = 1 + (dt*lambda/hbar)^2
Consequently, nonzero eigenmodes grow under this update: the displayed time-step heuristic is not a proof of stability or probability conservation. The current example illustrates the discretization and visualization, and must not be used as a validated unitary quantum solver. Check norm drift, spatial resolution, time resolution and periodic-boundary effects before interpreting numerical results.
The script uses a 151-by-151 grid with hbar=m=1, a Gaussian initial state and zero potential. It plots initial/final densities and writes wave_packet_evolution.mp4 in the current folder. VideoWriter needs a supported MPEG-4 encoder. The values are dimensionless model units, not a calibrated laboratory experiment.
This script plots three prescribed potential arrays: rectangular, elliptical and circular. It does not propagate a wavefunction or compute transmission/reflection probabilities. The finite rectangular region is assigned a positive potential, so the plotted example is a barrier rather than a negative potential well.
This is a separate split-step/directional-recursion example for a Gaussian packet and a circular barrier. It stores 80 time steps and generates density/potential panels plus 2DCylindricalPotential3D.gif. Its boundary handling and update are different from those of schrodingerequation_numerical.m; a stability claim for one method must not be transferred to the other.
These programs evolve wavefunctions and potentials. They do not implement Bohmian particle trajectories or an additional pilot-wave guidance equation. The repository name should not be read as a claim that such a trajectory solver is included.
wave_packet_evolution.mp4
Explore related repositories: Emergence · LorentzTransformations.
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