Numerical Solution of Schrödinger Equation by using Crank-Nicolson Method

Authors

  • J. Kafle Institute of Science and Technology, Central Department of Mathematics, T. U., Kritipur, Nepal
  • A. Kafle Institute of Science and Technology, Central Department of Mathematics, T. U., Kritipur, Nepal
  • C. N. Tiwari Institute of Science and Technology, Central Department of Mathematics, T. U., Kritipur, Nepal and Tri-Chandra Multiple Campus, Tribhuvan University, Ghantaghar, Nepal

DOI:

https://doi.org/10.3126/jnphyssoc.v9i1.57546

Keywords:

Schrödinger equation, Wave function, Quantum systems, Crank-Nicolson difference scheme

Abstract

The Schrödinger equation is a fundamental equation in quantum mechanics that describes how wave functions evolve over time. The study explored specific focus on the Crank-Nicolson scheme, which is widely used and efficient method. By applying these methods to the one-dimensional Schrödinger equation, the work provided insights into the behavior of these systems. To confirm the accuracy and reliability of this method, a test problem is solved. The result obtained from numerical method is compared with analytical solution. The graph of compared result is shown with the help of computational software. The test demonstrates that the method is effective for solving the Schrödinger equation, even when an analytical solution is not possible or too difficult to obtain. Overall, the Crank-Nicolson difference scheme is a valuable tool for understanding the behavior of quantum systems and solving problems.

Downloads

Download data is not yet available.
Abstract
99
PDF
62

Downloads

Published

2023-08-25

How to Cite

Kafle, J., Kafle, A., & Tiwari, C. N. (2023). Numerical Solution of Schrödinger Equation by using Crank-Nicolson Method. Journal of Nepal Physical Society, 9(1), 29–37. https://doi.org/10.3126/jnphyssoc.v9i1.57546

Issue

Vol. 9 No. 1 (2023)

Section

Articles

License

All right reserved. No part of this Journal may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval system, without permission in writing from the publisher, except by a reviewer who may quote brief passage in a review. The views and interpretation in this journal are those of author(s) and they are not attributable to the NPS.