Accurate numerical solutions of the time-dependent Schrödinger equation

We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schrödinger equation. The generalization yields numerical solutions accurate to order (Deltax)2r-1 in space and (Deltat)2M in time for any positive integers r and M, while...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2007-03, Vol.75 (3 Pt 2), p.036707-036707, Article 036707
Main Authors: van Dijk, W, Toyama, F M
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schrödinger equation. The generalization yields numerical solutions accurate to order (Deltax)2r-1 in space and (Deltat)2M in time for any positive integers r and M, while CN employ r=M=1. We note dramatic improvement in the attainable precision (circa ten or greater orders of magnitude) along with several orders of magnitude reduction of computational time. The improved method is shown to lead to feasible studies of coherent-state oscillations with additional short-range interactions, wave-packet scattering, and long-time studies of decaying systems.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.75.036707