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Matrix methods for radial Schrödinger eigenproblems defined on a semi-infinite domain

Author

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  • Aceto, Lidia
  • Magherini, Cecilia
  • Weinmüller, Ewa B.

Abstract

In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schrödinger equation posed on a semi-infinite interval. The original problem is first transformed to one defined on a finite domain by applying suitable change of the independent variable. The eigenvalue problem for the resulting differential operator is then approximated by a generalized algebraic eigenvalue problem arising after discretization of the analytical problem by the matrix method based on high order finite difference schemes. Numerical experiments illustrate the performance of the approach.

Suggested Citation

  • Aceto, Lidia & Magherini, Cecilia & Weinmüller, Ewa B., 2015. "Matrix methods for radial Schrödinger eigenproblems defined on a semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 179-188.
    • Handle: RePEc:eee:apmaco:v:255:y:2015:i:c:p:179-188
    DOI: 10.1016/j.amc.2014.05.075
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    Cited by:

    1. Mebirouk, AbdelMouemin & Bouheroum-Mentri, Sabria & Aceto, Lidia, 2020. "Approximation of eigenvalues of Sturm–Liouville problems defined on a semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Taher, Anis Haytham Saleh, 2024. "Highly accurate calculation of higher energy eigenvalues for the radial Schrödinger eigenproblems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 586-599.

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