A numerical method for the fractional Schrödinger type equation of spatial dimension two-Reference-Cited by-同舟云学术

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

Published:2013-03-19 Issue:2 Volume:16 Page:454-468
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Ford Neville¹,Manuela Rodrigues M.²,Vieira Nelson³

Affiliation:

1. Department of Mathematics, University of Chester, CH1 4BJ, Chester, England, UK

2. CIDMA — Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

3. CIDMA — Center for Research and Development in Mathematics and Applications and Polytechnical Institute of Leiria, School of Technology and Management, P-2411-901, Leiria, Portugal

Abstract

Abstract 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.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

http://link.springer.com/content/pdf/10.2478/s13540-013-0028-5.pdf

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