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：
暂无
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
收藏
页码：454 / 468
页数：14
相关论文
共 50 条
  • [41] Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation
    A. Konguetsof
    Journal of Mathematical Chemistry, 2010, 48 : 224 - 252
  • [42] A study of fractional Schrödinger equation composed of Jumarie fractional derivative
    JOYDIP BANERJEE
    UTTAM GHOSH
    SUSMITA SARKAR
    SHANTANU DAS
    Pramana, 2017, 88
  • [43] Structure preserving fourth-order difference scheme for the nonlinear spatial fractional Schr?dinger equation in two dimensions
    Ding, Hengfei
    Tian, Junhong
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 205 : 1 - 18
  • [44] Investigation of oxygen isotopes in the d-dimension schrödinger equation by the PNU method
    Jamshid, Khosravi Bijaeim
    Reza, Shojaei Mohammad
    Mohsen, Mousavi
    UPB Scientific Bulletin, Series C: Electrical Engineering and Computer Science, 2019, 81 (01): : 251 - 260
  • [45] An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension
    Anqi Chen
    Fengyan Li
    Yingda Cheng
    Journal of Scientific Computing, 2019, 78 : 772 - 815
  • [46] Legendre spectral collocation method for distributed and Riesz fractional convection–diffusion and Schrödinger-type equation
    M. A. Abdelkawy
    Mdi Begum Jeelani
    Abeer S. Alnahdi
    T. M. Taha
    E. M. Soluma
    Boundary Value Problems, 2022
  • [47] Global existence for the nonlinear fractional Schrödinger equation with fractional dissipation
    Darwich M.
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2018, 64 (2) : 323 - 334
  • [48] A split-step finite element method for the space-fractional Schrödinger equation in two dimensions
    Zhu, Xiaogang
    Wan, Haiyang
    Zhang, Yaping
    SCIENTIFIC REPORTS, 2024, 14 (01):
  • [49] Investigation of oxygen isotopes in the D-dimension schrödinger equation by the PNU method
    Jamshid, Khosravi Bijaeim
    Reza, Shojaei Mohammad
    Mohsen, Mousavi
    UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2019, 81 (01): : 251 - 260
  • [50] A variable-step Numerov method for the numerical solution of the Schrödinger equation
    Jesús Vigo-Aguiar
    Higinio Ramos
    Journal of Mathematical Chemistry, 2005, 37 : 255 - 262
12345