The initial wave packet is a (non-normalized) Gaussian function. It evolves over a period T along the x-axis. A potential is placed on its path.
Evolution of the wave packet for a Gaussian potential (more examples available in movies)
Snapshot of the wave packet for a step potential (more examples available in snapshots)
The program needs numpy and matplotlib to run. For movie generation, see the matplotlib.animation documentation (ffmpeg recommended).
You can clone the project in your current repository with:
$ git clone https://github.com/vguillon/time-dependent-schrodinger-equation.git
You can choose the parameters of the potentials directly in the potential_parameters.txt file. The parameters are:
Potential: select potential. Available potentials are 'step', 'barrier', 'well' and 'gaussian' ;V0: potential height. Only used for 'step', 'barrier' and 'well' ;width: potential width. Only used for 'barrier' and 'well'. Hints: for 'barrier',width= 0.03 and for 'well',width= 0.1 give good results ;x0: center of the gaussian potential ;sigma: width of the gaussian potential.
The program allows several command line options. Each of these options possess a default value. Hence, after the potential parameters are configured, you can just run
$ python3 schrodinger.py
to obtain a snapshot similare to the one above.
To show the available command line options, type:
$ python3 schrodinger.py -h
For instance, if you want a .png snapshot of the wave function after half a period for a wave packet starting at x=0.1 at t=0, you can write:
$ python3 schrodinger.py -sf png -t 0.5 -x 0.1
If you want to create a .mp4 movie over a period, type:
$ python3 schrodinger.py -o movie
If you want to create a .gif over a period with 3000 points along the x-axis for a wave packet starting at x=0.2 at t=0, write:
$ python3 schrodinger.py -o movie -mf gif -N 3000 -x 0.2
The generation of the datas can take few minutes.