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

Published

June 26, 2019

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

Pub Type

Journals

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DOI Link

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 December 5, 2024)