Vakgroep Toegepaste Wiskunde, Informatica en Statistiek

The numerical solutions of Sturm-Liouville and Schrödinger equations

Software developed by Toon Baeyens for his PhD-thesis (2023) Algorithms for time-independent Schr¨odinger equations

All developed software consists of C++-source files together with a python-package.
This python-package provides a user-friendly interface to the efficiently
implemented C++-code. To build upon this code, python is an optional
dependency. All Schrodinger problems can also be expressed using only C++.

Matslise 3.0 — pyslise

Solving one-dimensional Sturm–Liouville and Schr¨odinger problems with homogenous Robin or periodic boundary conditions. See chapter 2.

https://github.com/twist-numerical/matslise
https://pypi.org/project/pyslise/

Matslise 2D — pyslise2d

Approximating eigenvalues and eigenfunctions of two-dimensional Schrödinger problems on rectangular domains with homogenous Dirichlet boundary conditions,
using the method from chapter 3.

https://github.com/twist-numerical/matslise2d
https://pypi.org/project/pyslise2d/

Strands — strands

Approximating eigenvalues and eigenfunctions of two-dimensional Schr¨odinger
problems on general bounded domains with homogenous Dirichlet boundary
conditions, using the method from chapter 4.

https://github.com/twist-numerical/strands
https://pypi.org/project/Strands/

Software developed by Veerle Ledoux

Maple-files

  • CPM
    • Maple code which generates the expressions of the corrections for the CPM{P,N} methods: CPM.mws (Maple 8). See Appendix C in V. Ledoux, M. Van Daele and G. Vanden Berghe, CP methods of higher order for Sturm-Liouville and Schrodinger equations, Comp. Phys. Comm. 162 (2004) 151 - 165.
  • LPM
    • Maple code which generates the expressions of the first and second order correction for the LPM[4,1] and LPM[4,2] method: LPManalyt.mw (Maple 9.5) or LPManalyt.mws (Maple 8).
    • Maple code which generates the asymptotic expansions of the zeroth, first and second order correction for the LPM[4], LPM[4,1] and LPM[4,2] method: LPMasymp.mw (Maple 9.5) or LPMasymp.mws (Maple 8).

MATSLISE

  • MATSLISE: graphical Matlab software package for the numerical solution of one-dimensional Sturm-Liouville and Schrodinger problems. A CPM{P,N} of high order is applied to compute the eigenvalues and eigenfunctions. The graphical user interface allows one to enter the input in a straightforward manner, to control certain parameters interactively and to present the results graphically.
  • MATSLISE_AD: This version of MATSLISE does not need the Matlab symbolic toolbox. Automatic differentiation is used to perform the Liouville transformation.

LPM-implementations

  • See: V. Ledoux, M. Rizea, L. Gr. Ixaru, G. Vanden Berghe and M. Van Daele, Solution of the Schrödinger equation by a high order perturbation method based on a linear reference potential, Comp. Phys. Comm. 175 (2006) 424 - 439.
  • lpm42ws.f and params.dat: The Fortran77 implementation of the LPM[4,2] method applied on a Woods-Saxon problem.
  • LPMmatlab: This Matlab package uses the LPM[4,2] method to compute eigenvalues of a regular Schrodinger problem.

The numerical solution of multichannel Schrodinger problems

  • MATCAS: a Matlab tool for the automatic computation of bound-state eigenvalues and wavefunctions of coupled Schrodinger equations. See V. Ledoux, M. Van Daele, Automatic computation of quantum-mechanical bound states and wavefunctions (2012).
  • MATSCS: Matlab package implementing the CPM{P,N} methods for the numerical solution of the multichannel Schrodinger eigenvalue problem. See V. Ledoux, M. Van Daele and G. Vanden Berghe, A numerical procedure to solve the multichannel Schrodinger eigenvalue problem, Comp. Phys. Comm. (2006).
  • sysper.f, sysdop.f, sys.inp, params: Fortran programs solving a system with a deformed potential leading to an eigenvalue problem where the required eigenvalue is related to the potential adjusting, viz, the eigenvalue is the depth of the potential. This problem is considered in: V. Ledoux, M. Rizea, M. Van Daele, G. Vanden Berghe and I. Silisteanu, Eigenvalue problem for a coupled channel Schrodinger equation with application to the description of deformed nuclear systems (2008).

Modified integral series methods

  • MATSLEMN : Matlab implementation of the sixth order modified Neumann method for the numerical solution of Sturm-Liouville problems.