Advanced search
1 file | 519.88 KB Add to list

The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations

Toon Baeyens (UGent) and Marnix Van Daele (UGent)
Author
Organization
Abstract
In this paper, we present the basic routines of the C++-program Matslise 3.0, an updated but yet restricted version of the matlab package Matslise 2.0. Matslise 3.0 currently allows the accurate, but in comparison to Matslise 2.0, faster computation of eigenvalues and eigenfunctions of one dimensional time-independent Schrödinger problems. The numerical examples show that speed up factors up to 20 (for the eigenvalues) and 200 (for the eigenfunctions) are obtained. These highly optimized routines will enable us, in the near future, to extend Matslise 3.0 to solve time-independent 2D and 3D as well as time-dependent 1D problems.
Keywords
Schrödinger equation, Sturm–Liouville problems, Constant Perturbations Methods, Eigenvalues, Eigenfunctions

Downloads

  • (...).pdf
    • full text (Published version)
    • |
    • UGent only
    • |
    • PDF
    • |
    • 519.88 KB

Citation

Please use this url to cite or link to this publication:

MLA
Baeyens, Toon, and Marnix Van Daele. “The Fast and Accurate Computation of Eigenvalues and Eigenfunctions of Time-Independent One-Dimensional Schrödinger Equations.” COMPUTER PHYSICS COMMUNICATIONS, vol. 258, 2020, doi:10.1016/j.cpc.2020.107568.
APA
Baeyens, T., & Van Daele, M. (2020). The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations. COMPUTER PHYSICS COMMUNICATIONS, 258. https://doi.org/10.1016/j.cpc.2020.107568
Chicago author-date
Baeyens, Toon, and Marnix Van Daele. 2020. “The Fast and Accurate Computation of Eigenvalues and Eigenfunctions of Time-Independent One-Dimensional Schrödinger Equations.” COMPUTER PHYSICS COMMUNICATIONS 258. https://doi.org/10.1016/j.cpc.2020.107568.
Chicago author-date (all authors)
Baeyens, Toon, and Marnix Van Daele. 2020. “The Fast and Accurate Computation of Eigenvalues and Eigenfunctions of Time-Independent One-Dimensional Schrödinger Equations.” COMPUTER PHYSICS COMMUNICATIONS 258. doi:10.1016/j.cpc.2020.107568.
Vancouver
1.
Baeyens T, Van Daele M. The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations. COMPUTER PHYSICS COMMUNICATIONS. 2020;258.
IEEE
[1]
T. Baeyens and M. Van Daele, “The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations,” COMPUTER PHYSICS COMMUNICATIONS, vol. 258, 2020.
@article{8672636,
  abstract     = {In this paper, we present the basic routines of the C++-program Matslise 3.0, an updated but yet restricted version of the matlab package Matslise 2.0. Matslise 3.0 currently allows the accurate, but in comparison to Matslise 2.0, faster computation of eigenvalues and eigenfunctions of one dimensional time-independent Schrödinger problems. The numerical examples show that speed up factors up to 20 (for the eigenvalues) and 200 (for the eigenfunctions) are obtained. These highly optimized routines will enable us, in the near future, to extend Matslise 3.0 to solve time-independent 2D and 3D as well as time-dependent 1D problems.},
  articleno    = {107568},
  author       = {Baeyens, Toon and Van Daele, Marnix},
  issn         = {0010-4655},
  journal      = {COMPUTER PHYSICS COMMUNICATIONS},
  keywords     = {Schrödinger equation,Sturm–Liouville problems,Constant Perturbations Methods,Eigenvalues,Eigenfunctions},
  language     = {eng},
  pages        = {9},
  title        = {The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations},
  url          = {http://dx.doi.org/10.1016/j.cpc.2020.107568},
  volume       = {258},
  year         = {2020},
}

Altmetric
View in Altmetric