Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 11, 17 November 2023
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Solution and numerical analysis of two-dimensional time-independent Schrödinger equation based on finite difference method
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Abstract
With the continuous development and widespread use of quantum mechanics, solving the Schrödinger equation has become a hot research topic. The finite difference method has the advantages of simple calculation and high accuracy, which means that it has high potential in solving the numerical solutions of the Schrödinger equation. In this paper, we deeply explore the problem of using the finite difference method to solve the numerical solution of the time-independent Schrödinger equation, propose a solution method based on the finite difference method, and evaluate its performance under different conditions. Firstly, by analyzing the principles and characteristics of the finite difference method, we construct a difference format for the time-independent Schrödinger equation. Then, by converting the difference format of the numerical solutions of the equation into a matrix, the numerical calculation problem is transformed into a matrix eigenvalue and eigenvector problem. Finally, for different physical scenarios, the established model is numerically solved and its performance is analyzed. This study found that the constructed numerical solution method exhibits high accuracy and stability in solving the numerical solutions of the time-independent Schrödinger equation. In different physical scenarios, this method can provide satisfactory results, thus verifying the feasibility of applying the finite difference method to this problem.
Keywords
finite difference method, Schrödinger equation, numerical solution, eigenvalue.
References
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
- ISBN (Print)
- 978-1-83558-133-9
- ISBN (Online)
- 978-1-83558-134-6
- Published Date
- 17 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/11/20230388
- Copyright
- 17 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited