Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Comparison of Numerical Approaches to the Time-Dependent Schrodinger Solutions in One Dimension

Published

Author(s)

Heman Gharibnejad, Barry I. Schneider, Mark Leadingham, henry Schmale

Abstract

We examine the performance of various time propagation schemes using a one-dimensional model of the hydrogen atom. In this model, the exact coulomb potential is replaced by a soft-core interaction. The model has been shown to be a reasonable representation of what occurs in the fully three dimensional hydrogen atom. Our results show that while many numerically simple (low order) propagation schemes work, they often require quite small time steps. Comparing them against more accurate methods, which may require more work per time step but allow much larger time steps, can be illuminating. We show that at least in this problem, the compute time for a number of the more accurate methods is actually less than lower order schemes. Finally, we make some remarks on what to expect in generalizing our findings to more than one dimension.
Citation
Computer Physics Communications

Keywords

Time Dependent Schrodinger Equation, one-dimensional hydrogen, numerical methods

Citation

Gharibnejad, H. , Schneider, B. , Leadingham, M. and Schmale, H. (2019), Comparison of Numerical Approaches to the Time-Dependent Schrodinger Solutions in One Dimension, Computer Physics Communications, [online], https://doi.org/10.1016/j.cpc.2019.05.019 (Accessed September 23, 2021)
Created June 26, 2019, Updated August 20, 2019