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

被引：30

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

页码：454 / 468

页数：15

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