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

被引：28
|
作者：
Ford, Neville J. [1 ]
Manuela Rodrigues, M. [2 ]
Vieira, Nelson [3 ,4 ]
机构：
[1] Univ Chester, Dept Math, Chester CH1 4BJ, Cheshire, England
[2] Univ Aveiro, Dept Math, CIDMA Ctr Res & Dev Math & Applicat, P-3810193 Aveiro, Portugal
[3] CIDMA Ctr Res & Dev Math & Applicat, P-2411901 Leiria, Portugal
[4] Polytech Inst Leiria, Sch Technol & Management, P-2411901 Leiria, Portugal
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2013年 / 16卷 / 02期
关键词：
fractional partial differential equation; fractional Schrodinger equation; finite difference method; stability; Mittag-Leffler function; FINITE-PART INTEGRALS; QUANTUM-MECHANICS;
D O I：
10.2478/s13540-013-0028-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work focuses on an investigation of the (n+1)-dimensional time-dependent fractional Schrodinger 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
收藏
页码：454 / 468
页数：15
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