Numerical Solution of Schrödinger Equation by Crank–Nicolson Method-Reference-Cited by-同舟云学术

Numerical Solution of Schrödinger Equation by Crank–Nicolson Method

Published:2022-04-14 Issue: Volume:2022 Page:1-11
ISSN:1563-5147
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Khan Amin¹,Ahsan Muhammad¹,Bonyah Ebenezer²^ORCID,Jan Rashid¹^ORCID,Nisar Muhammad³⁴,Abdel-Aty Abdel-Haleem⁵⁶^ORCID,Yahia Ibrahim S.⁷⁸⁹

Affiliation:

1. Department of Mathematics, University of Swabi, Swabi 23430, KPK, Pakistan

2. Department of Mathematics Education, Akenten Appiah Menka University of Skills Traning and Enterprises Development, Kumasi, Ghana

3. Department of Mathematics Statiscs, Macquaire University Sydney, NSW2109, Australia

4. Department of Mathematics, FATA University, Darra Adam Khel 26100, Pakistan

5. Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

6. Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

7. Laboratory of Nano-Smart Materials for Science and Technology(LNSMST), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

8. Research Center for Advanced Materials Science (RCAMS), King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

9. Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Semiconductor Lab, Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt

Abstract

In this study, we implemented the well-known Crank–Nicolson scheme for the numerical solution of Schrödinger equation. The numerical results converge to the exact solution because the Crank–Nicolson scheme is unconditionally stable and accurate. We have compared the results for different parameters with analytical solution, and it is found that the Crank–Nicolson scheme is suitable for the numerical solution of Schrödinger equations. Three different problems are included to verify the accuracy, stability, and capability of the Crank–Nicolson scheme.

Funder

King Khalid University

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2022/6991067.pdf

Reference31 articles.

1. Finite difference methods;G. E. Forsythe;Partial Differential,1960

2. Any l-state solutions of the Schrodinger equation interacting with Hellmann–Kratzer potential model

3. On the existence of positive solutions of ordinary differential equations

4. Review of tsunami simulation with a finite difference method;F. Imamura;Long-wave runup models,1996

5. Learning data-driven discretizations for partial differential equations

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A full spectrum of optical solitons for the concatenation model;Nonlinear Dynamics;2023-11-06

2. Soft Computing Artificial Intelligence of Schrödinger Time Independent Equation Arises in Wheeler–DeWitt Model of Quantum Cosmology;Computational Mathematics and Mathematical Physics;2023-11

3. Stability, convergence and error analysis of B-spline collocation with Crank–Nicolson method and finite element methods for numerical solution of Schrodinger equation arises in quantum mechanics;Physica Scripta;2023-10-13