A numerical method for the fractional Schrödinger type equation of spatial dimension two

被引：0
|
作者：
Neville J. Ford
M. Manuela Rodrigues
Nelson Vieira
机构：
[1] University of Chester,Department of Mathematics
[2] University of Aveiro Campus Universitário de Santiago,CIDMA — Center for Research and Development in Mathematics and Applications Department of Mathematics
[3] School of Technology and Management,CIDMA — Center for Research and Development in Mathematics and Applications and Polytechnical Institute of Leiria
来源：
Fractional Calculus and Applied Analysis | 2013年 / 16卷
关键词：
fractional partial differential equation; fractional Schrödinger equation; finite difference method; stability; Mittag-Leffler function; Primary 35R11; Secondary 42A38, 33E12, 65M06, 47H10;
D O I：
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中图分类号：
学科分类号：
摘要：
This work focuses on an investigation of the (n+1)-dimensional time-dependent fractional Schrödinger type equation. In the early part of the paper, the wave function is obtained using Laplace and Fourier transform methods and a symbolic operational form of the solutions in terms of Mittag-Leffler functions is provided. We present an expression for the wave function and for the quantum mechanical probability density. We introduce a numerical method to solve the case where the space component has dimension two. Stability conditions for the numerical scheme are obtained.
引用
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页码：454 / 468
页数：14
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