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arXiv · 1709.09800

Non-standard FDTD implementation of the Schrödinger equation

José Manuel Nápoles-Duarte·Marco Antonio Chavez-Rojo
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Abstract

In this work, we apply the Cole's non-standard form of the FDTD to solve the time dependent Schrödinger equation. We deduce the equations for the non-standard FDTD considering an electronic wave function in the presence of potentials which can be higher or lower in comparison with the energy of the electron. The non-standard term is found to be almost the same, except for a sine functions which is transformed to a hyperbolic sine function,as the argument is imaginary when the potential has higher energy than the electron. Perfectly Matched Layers using this methodology are also presented.

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José Manuel Nápoles-Duarte, Marco Antonio Chavez-Rojo. 2017-09-28. Non-standard FDTD implementation of the Schrödinger equation. https://arxiv.org/abs/1709.09800

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