Bulletin of the American Physical Society
APS New England Section 2018 Fall Meeting
Volume 63, Number 21
Friday–Saturday, November 2–3, 2018; University of Massachusetts Dartmouth, Dartmouth, Massachusetts
Session B01: Poster Session
5:00 PM,
Friday, November 2, 2018
Library
Room: Living Room
Abstract ID: BAPS.2018.NEF.B01.18
Abstract: B01.00018 : Modified Finite Difference Method on the 1-D Schrodinger Equation*
Presenter:
Trevor A A Robertson
(University of Massachusetts Dartmouth)
Authors:
Trevor A A Robertson
(University of Massachusetts Dartmouth)
Jonathan Pierre-Louis
(University of Massachusetts Dartmouth)
Jay Wang
(University of Massachusetts Dartmouth)
The time-dependent Schrödinger equation (TDSE) is a fundamental law in understanding the states of many microscopic systems. Such systems occur in nearly all branches of physics and engineering, including atomic, high-energy, and solid-state physics just to name a few. A robust and efficient algorithm to solve the TDSE would be an essential goal in these respective fields. In this study we use the well-known method for solving the TDSE, the finite difference method (FDM) but with an important modification: formulating the TDSE in a form suitable for symplectic integration to conserve flux. In this presentation we discuss case studies and present results on stability, flux conservation, as well as scattering probabilities in 1D potentials. We show that the modified method is a stable, promising, and accurate method for linear domains over lower dimensions with arbitrary potentials. We also discuss challenging problems of scaling to higher dimensions and more refined grids.
*This work was thanks to funding from the Massachusetts Space Grant Consortium.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.NEF.B01.18
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