SiegPy: "Siegert states with Python"

This module provides the tools to find the numerical Siegert (or resonant) states of 1D potentials with compact support, as well as the analytical ones of the 1D Square-Well Potential:

>>> from siegpy import SWPBasisSet, SWPotential
>>> pot = SWPotential(5, 5)
>>> siegerts = SWPBasisSet.find_Siegert_states(pot, re_k_max=5, im_k_max=2, step_re=3)
>>> len(siegerts)
18
>>> siegerts.plot_energies()
>>> siegerts.plot_wavefunctions()

A basis set made of such states is discrete and can later be compared to the exact results (i.e. using bound and continuum states) for:

• its completeness, compared to a basis set using the usual continuum states,
• its ability to reproduce the response function (i.e., to provide an approximation of the Green's function with discrete states),
• its ability to reproduce the time-propagation of an initial wavepacket.

>>> from siegpy import Rectangular
>>> r = Rectangular(-1.5, 1.5)
>>> siegerts.plot_completeness_convergence(r)
>>> time_grid = [0, 0.1, 0.25, 0.5, 1.0, 2.0, 3.0]
>>> import numpy as np
>>> xgrid = np.linspace(-3, 3, 201)
>>> siegerts.grid = xgrid
>>> siegerts.Siegert_propagation(r, time_grid)

Installation

Currently, git clone this repository and run pip install . in the SiegPy folder.

This module requires Python3.4+ and the following packages, which will be installed while running the previous command if necessary:

• numpy
• scipy
• matplotlib
• mpmath

Documentation

The documentation can be found here.

Ipython notebooks are stored in the 'doc/notebooks' folder and are part of the documentation as tutorials for the SiegPy module. They can also be considered as an introduction to the Siegert states. They are supposed to be read in a specific order, which can be is given in the doc/notebooks.rst file.

The whole documentation can be compiled manually. This requires the installation of the some extra packages (such as sphinx, nbsphinx, sphinx_rtd_theme, ...). This can be done by running pip install .[doc]. You can then go in the doc folder and running the make html command (or alternatively python3 -m sphinx . build -jN, where N is the number of precessors used for the compilation). This command creates the code documentation and runs all the notebooks in order to create a tutorial.

For developpers

For developpers:

• Run pip3 install -e .[test] to get all the packages required for testing. Running pytest in the SiegPy folder will then launch all the tests.
  • Unit tests are performed using pytest.
  • pytest-cov shows which part of the code is currently not covered by unit tests (this is performed by running the pytest command).
  • flake8 is the tool used to check for PEP8 compliance (run flake8 in the SiegPy folder).
• If you modify notebooks, install and use nbstripout in order to clean the ouput cells before each git commit to save memory on the repository. See https://github.com/kynan/nbstripout for details.
• Documentation is created using sphinx (http://www.sphinx-doc.org/). The use of restructured text in the docstrings is therefore recommended.