A simulation of quantum tunnelling created with numpy, scipy, and matplotlib in Python. In the default simulation, a Gaussian wave packet can be seen tunnelling through a potential barrier approximately 3000x its maximum amplitude. The time dependent Schrodinger equation is solved as an eigenvalue problem and the solution is reconstructed through the weighted sums of the time-independent energy eigenvalues and eigenstates, which are multiplied by a time dependent phase factor.
This project is done in Jupyter, but can also be run in any Python interpreter with the correct dependencies installed.
To install Jupyter, head to https://jupyter.org/install.
Otherwise, to install the necessary libraries:
pip install numpy scipy matplotlib
Rectangular barrier
Finite square well. Interestingly, the simulation seems to converge to the time independent solution consisting of standing waves.
Quadratic potential
Other examples (the Lennard-Jones and Wood-Saxon potentials) can be found in the examples folder.
This project was mainly inspired by this YouTube from Mr. P Solver, as well as various other online sources.
- The edges reflect the wavefunction, interfering with the simulation in the middle
- The GIF files produced have a massive file size before compression
- Python 3.7.3
- Jupyter core 4.6.3