Solving the Schrodinger equation using the finite difference time domain method

被引：66
|
作者：
Sudiarta, I. Wayan [1 ]
Geldart, D. J. Wallace
机构：
[1] Dalhousie Univ, Dept Phys & Atmospher Sci, Halifax, NS B3H 3J5, Canada
[2] Univ New S Wales, Sch Phys, Sydney, NSW 2052, Australia
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2007年 / 40卷 / 08期
关键词：
D O I：
10.1088/1751-8113/40/8/013
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we solve the Schrodinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schrodinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems.
引用
收藏
页码：1885 / 1896
页数：12
相关论文
共 50 条
  • [41] FINITE-DIFFERENCE SCHRODINGER EQUATION
    CALDIROLA, P
    [J]. LETTERE AL NUOVO CIMENTO, 1976, 17 (14): : 461 - 464
  • [42] Finite Difference Method for an Optimal Control Problem for a Nonlinear Time-dependent Schrodinger Equation
    Aksoy, Nigar Yildirim
    Dinh Nho Hao
    Yagub, Gabil
    [J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (06) : 799 - 817
  • [43] Finite difference method for solving the Schrodinger equation with band nonparabolicity in mid-infrared quantum cascade lasers
    Cooper, J. D.
    Valavanis, A.
    Ikonic, Z.
    Harrison, P.
    Cunningham, J. E.
    [J]. JOURNAL OF APPLIED PHYSICS, 2010, 108 (11)
  • [44] Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrodinger equation
    Tay, Wei Choon
    Tan, Eng Leong
    [J]. COMPUTER PHYSICS COMMUNICATIONS, 2014, 185 (07) : 1886 - 1892
  • [45] Pseudospectral Time Domain Method Implementation Using Finite Difference Time Stepping
    Gunes, Ahmet
    Aksoy, Serkan
    [J]. IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, 2018, 28 (05) : 365 - 367
  • [46] Efficient finite difference solutions to the time-dependent Schrodinger equation
    Nash, PL
    Chen, LY
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 130 (02) : 266 - 268
  • [47] The symplectic finite difference time domain method
    Saitoh, I
    Suzuki, Y
    Takahashi, N
    [J]. IEEE TRANSACTIONS ON MAGNETICS, 2001, 37 (05) : 3251 - 3254
  • [48] Sparse Finite Difference Time Domain Method
    Doerr, Christopher R.
    [J]. IEEE PHOTONICS TECHNOLOGY LETTERS, 2013, 25 (23) : 2259 - 2262
  • [49] FINITE DIFFERENCE METHOD FOR SOLVING HEAT CONDUCTION EQUATION OF THE GRANITE
    Maturi, Dalal Adnan
    Aljedani, Amal Ibrahem
    Alaidarous, Eman Salem
    [J]. INTERNATIONAL JOURNAL OF GEOMATE, 2019, 17 (61): : 135 - 140
  • [50] A Finite Difference Method for Solving the Wave Equation with Fractional Damping
    Cui, Manruo
    Ji, Cui-Cui
    Dai, Weizhong
    [J]. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS, 2024, 29 (01)
12345