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

Ford, Neville J.; Rodrigues, M. Manuela; Vieira, Nelson

http://hdl.handle.net/10400.8/15851

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Autores

Ford, Neville J.

Rodrigues, M. Manuela

Vieira, Nelson

Resumo(s)

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.

Palavras-chave

Finite difference method Fractional partial differential equation Fractional Schrödinger equation Mittag-Leffler function

URI

http://hdl.handle.net/10400.8/15851

Citação

Ford, N.J., Manuela Rodrigues, M. & Vieira, N. A numerical method for the fractional Schrödinger type equation of spatial dimension two. fcaa 16, 454–468 (2013). https://doi.org/10.2478/s13540-013-0028-5

Projetos de investigação

Strategic Project - UI 4106 - 2011-2012

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Editora

Springer

DOI

10.2478/s13540-013-0028-5

Coleções

ESTG - Artigos em revistas internacionais

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