Numerical Solution of Schrödinger Equation by Crank-Nicolson Method

Amin Khan; Muhammad Ahsan; Ebenezer Bonyah; Rashid Jan; Muhammad Nisar; Abdel Haleem Abdel-Aty; Ibrahim S. Yahia

doi:10.1155/2022/6991067

Numerical Solution of Schrödinger Equation by Crank-Nicolson Method

Amin Khan
, Muhammad Ahsan
, Ebenezer Bonyah
, Rashid Jan
, Muhammad Nisar
, Abdel Haleem Abdel-Aty
, Ibrahim S. Yahia

King Khalid University
Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development
Macquarie University
Fata University Of Bisha
University of Bisha
Al-Azhar University
Ain Shams University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Article number	6991067
Journal	Mathematical Problems in Engineering
Volume	2022
DOIs	https://doi.org/10.1155/2022/6991067
State	Published - 2022
Externally published	Yes

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10.1155/2022/6991067

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title = "Numerical Solution of Schr{\"o}dinger Equation by Crank-Nicolson Method",

abstract = "In this study, we implemented the well-known Crank-Nicolson scheme for the numerical solution of Schr{\"o}dinger 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 Schr{\"o}dinger equations. Three different problems are included to verify the accuracy, stability, and capability of the Crank-Nicolson scheme.",

author = "Amin Khan and Muhammad Ahsan and Ebenezer Bonyah and Rashid Jan and Muhammad Nisar and Abdel-Aty, \{Abdel Haleem\} and Yahia, \{Ibrahim S.\}",

note = "Publisher Copyright: {\textcopyright} 2022 Amin Khan et al.",

year = "2022",

doi = "10.1155/2022/6991067",

language = "English",

volume = "2022",

journal = "Mathematical Problems in Engineering",

issn = "1024-123X",

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T1 - Numerical Solution of Schrödinger Equation by Crank-Nicolson Method

AU - Khan, Amin

AU - Ahsan, Muhammad

AU - Bonyah, Ebenezer

AU - Jan, Rashid

AU - Nisar, Muhammad

AU - Abdel-Aty, Abdel Haleem

AU - Yahia, Ibrahim S.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85129201161

U2 - 10.1155/2022/6991067

DO - 10.1155/2022/6991067

M3 - Article

AN - SCOPUS:85129201161

SN - 1024-123X

VL - 2022

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

M1 - 6991067

ER -

Numerical Solution of Schrödinger Equation by Crank-Nicolson Method

Abstract

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