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
  • [21] Travelling Waves for the Nonlinear Schrödinger Equation with General Nonlinearity in Dimension Two
    David Chiron
    Claire Scheid
    Journal of Nonlinear Science, 2016, 26 : 171 - 231
  • [22] An efficient meshless numerical method with the error estimate for two-dimensional Schrödinger equation
    Habibirad, Ali
    Baghani, Omid
    Azin, Hadis
    Zaferanieh, Mehdi
    Inc, Mustafa
    APPLIED NUMERICAL MATHEMATICS, 2024, 202 : 143 - 157
  • [23] Time and Space Fractional Schrdinger Equation with Fractional Factor
    相培
    郭永新
    傅景礼
    Communications in Theoretical Physics, 2019, 71 (01) : 16 - 26
  • [24] Numerical Simulation of Nonlinear Schrödinger Equation in One and Two Dimensions
    Geeta Arora
    Joshi V.
    Mittal R.C.
    Mathematical Models and Computer Simulations, 2019, 11 (4) : 634 - 648
  • [25] Schrödinger equation in dimension two with competing logarithmic self-interactionSchrödinger equation in dimension...A. Azzollini et al.
    Antonio Azzollini
    Pietro d’Avenia
    Alessio Pomponio
    Calculus of Variations and Partial Differential Equations, 2025, 64 (4)
  • [26] Numerical Study of Schrödinger Equation Using Differential Quadrature Method
    Bhatia R.
    Mittal R.C.
    International Journal of Applied and Computational Mathematics, 2018, 4 (1)
  • [27] Numerical Solution of Schrödinger Equation by Crank-Nicolson Method
    Khan, Amin
    Ahsan, Muhammad
    Bonyah, Ebenezer
    Jan, Rashid
    Nisar, Muhammad
    Abdel-Aty, Abdel-Haleem
    Yahia, Ibrahim S.
    Mathematical Problems in Engineering, 2022, 2022
  • [28] Application of Improved SPH Method in Solving Time Fractional Schrödinger Equation
    Ma, Luyang
    Imin, Rahmatjan
    INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2024, 21 (06)
  • [29] Beam propagation management in a fractional Schrödinger equation
    Changming Huang
    Liangwei Dong
    Scientific Reports, 7
  • [30] Memory effect in time fractional Schr?dinger equation
    祖传金
    余向阳
    Chinese Physics B, 2024, 33 (02) : 253 - 258
12345