QmPy is a python package containing routines to numerically solve and visualize the schroedinger equation for different potentials. Its main purpose is to support an executable script called qmsolve which combines the functionalities above.

Disclaimer

This is a student project. It utilizes very unstable and simple numerical algorithms.

Requirements

This package requires Python 3.6 or higher and the packages numpy, scipy and matplotlib.

Installation

For easy installation with pip use:

pip install -i https://test.pypi.org/simple/ qmpy-schrodinger

Usage

Using the script

Information for legacy users

In terms of the restructuring in release 3.0.0, the configuration file format was changed to json. An additional script is included to convert legacy configuration files to the new syntax.

./parse_legacy_config old_config_filename.inp

Usage

The script requires a configuration file which contains all the necessary information about the quantum mechanical system. The data is provided in json format. By default the script will search for a file 'qmsolve_config.json'. An example of such a file is included below.

{
  "computation": {
    "mass": 4.0,
    "xrange": {
      "xmin": -20.0,
      "xmax":  20.0,
      "npoint": 1999
    },
    "evrange": [1, 10],
    "interpolation.type": "cspline",
    "potential": {
      "x.values": [-20.0, -10.0, 0.0, 10.0, 20.0],
      "y.values": [35.0, 0.0, 2.0, 0.0, 35.0]
    }
  },
  "visualisation": {
    "autoscale": true,
    "scale": null,
    "xlim": null,
    "ylim": null
  }
}

The field 'visualisation' is entirely optional and just for customisation purposes. The script can be run via the command line by using

./qmsolve

It supports computing energies, wavefunctions and expected values for the x-coordinate, which is invoked with the command ./qmsolve compute. The results may also be visualized by using ./qmsolve visualise. It also takes numerous optional arguments which will be listed when using the -h option with one of the commands.

Using the modules

Calculating the first four energies and wavefunctions of a particle in a box aswell as the expected values and uncertainties for the x-xoordinate for each state.

from qmpy.solvers import schroedinger, calculate_expval, calculate_uncertainty
from numpy import linspace, zeros

mass = 2.0
xcords = linspace(-2, 2, 1999)
pot = zeros((1999, ))

vals = {'mass': mass,
        'xcords': xcords,
        'potential': pot}

# returns the first four energies and wavefunctions
energies, wfuncs = schroedinger(vals, select_range=(0, 3))

# calculate the expected value for the x-coordinate for each state
expvals = calculate_expval(xcoords, wfuncs)

# calculate the uncertainty of the x-coordinate for each state
uncs = calculate_uncertainty(xcoords, wfuncs)

Plotting numerical data contained in a directory

from qmpy.graphics import qm_plot

# directory containing the files potential.dat, energies.dat,
# wavefuncs.dat, and expvalues.dat.
datadir = 'myqmdata/'

# plot the data and save the plot as 'my_plot.png'
qm_plot(datadir, sname='my_plot.png')

Documentation

The documentation can be found at kenokrieger.com/code_projects/qmpy.

Tests

Tests for the package are located in the tests/ directory. The tests can all be run via pytest through the command line (python3 -m pytest in the highest directory; you may need to update your PYTHONPATH accordingly).

Contributing

Contributions are always welcome. To contribute fork the repository from github and develop your feature including unit tests. For your contribution to be incorporated in the main build issue a pull request.

License

BSD 2-Clause License
See LICENSE.txt for further information.