A finite-difference method for the one-dimensional time-dependent schrödinger equation on unbounded domain

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2005.05.006 ◽

2005 ◽

Vol 50 (8-9) ◽

pp. 1345-1362 ◽

Author(s):

Houde Han ◽

Jicheng Jin ◽

Xiaonan Wu

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Unbounded Domain ◽

Difference Method ◽

Schrodinger Equation ◽

Time Dependent ◽

One Dimensional ◽

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An Efficient Second-Order Finite Difference Method for the One-Dimensional Schrödinger Equation with Absorbing Boundary Conditions

SIAM Journal on Numerical Analysis ◽

10.1137/17m1122347 ◽

2018 ◽

Vol 56 (2) ◽

pp. 766-791 ◽

Author(s):

Buyang Li ◽

Jiwei Zhang ◽

Chunxiong Zheng

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Boundary Conditions ◽

Difference Method ◽

Schrodinger Equation ◽

Absorbing Boundary Conditions ◽

Second Order ◽

Absorbing Boundary ◽

One Dimensional ◽

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Finite Difference Method for an Optimal Control Problem for a Nonlinear Time-dependent Schrödinger Equation

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2016.1266656 ◽

2016 ◽

Vol 38 (6) ◽

pp. 799-817 ◽

Author(s):

Nigar Yıldırım Aksoy ◽

Dinh Nho Hào ◽

Gabil Yagub

Keyword(s):

Optimal Control ◽

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Optimal Control Problem ◽

Control Problem ◽

Difference Method ◽

Schrodinger Equation ◽

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Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Communications in Theoretical Physics ◽

10.1088/1572-9494/ab6185 ◽

2020 ◽

Vol 72 (2) ◽

pp. 025001

Author(s):

Bin Cheng ◽

Ya-Ming Chen ◽

Chuan-Fu Xu ◽

Da-Li Li ◽

Xiao-Gang Deng

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Dirac Delta ◽

Delta Potential ◽

Dirac Delta Potential

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Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

Nonlinear Dynamics ◽

10.1007/s11071-021-06249-x ◽

2021 ◽

Vol 103 (3) ◽

pp. 2493-2507

Author(s):

Ahmed S. Hendy ◽

Mahmoud A. Zaky

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Fractional Schrödinger Equation ◽

Graded Meshes ◽

Nonlinear Fractional Schrödinger Equation ◽

Fractional Schrodinger Equation

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A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-016-0704-x ◽

2016 ◽

Vol 55 (3) ◽

pp. 697-716 ◽

Author(s):

Jianbin Zhao ◽

T. E. Simos

Keyword(s):

Approximate Solution ◽

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Algebraic Order

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A comparative numerical study based on cubic exponential B-splines and finite difference method for the nonlinear Schrödinger equation

10.1063/1.5136440 ◽

2019 ◽

Author(s):

Azhar Ahmad ◽

Amirah Azmi ◽

Nur Nadiah Abd Hamid ◽

Ahmad Izani Md. Ismail

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Numerical Study ◽

Nonlinear Schrodinger Equation ◽

B Splines ◽

Nonlinear Schrödinger

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A finite-difference method for the numerical solution of the Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(96)00156-2 ◽

1997 ◽

Vol 79 (2) ◽

pp. 189-205 ◽

Author(s):

T.E. Simos ◽

P.S. Williams

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Numerical Solution ◽

Difference Method ◽

Schrodinger Equation

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Finite difference method for solving the Schrödinger equation with band nonparabolicity in mid-infrared quantum cascade lasers

Journal of Applied Physics ◽

10.1063/1.3512981 ◽

2010 ◽

Vol 108 (11) ◽

pp. 113109 ◽

Author(s):

J. D. Cooper ◽

A. Valavanis ◽

Z. Ikonić ◽

P. Harrison ◽

J. E. Cunningham

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Quantum Cascade Lasers ◽

Mid Infrared ◽

Quantum Cascade ◽

Cascade Lasers ◽

Band Nonparabolicity

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An analysis of the finite-difference method for one-dimensional Klein–Gordon equation on unbounded domain

Applied Numerical Mathematics ◽

10.1016/j.apnum.2008.10.005 ◽

2009 ◽

Vol 59 (7) ◽

pp. 1568-1583 ◽

Author(s):

Houde Han ◽

Zhiwen Zhang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Unbounded Domain ◽

Difference Method ◽

Gordon Equation ◽

One Dimensional ◽

Klein Gordon ◽

The Finite Difference Method ◽

Klein Gordon Equation

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Finite difference method with cubic spline for solving nonlinear schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207169608804528 ◽

1996 ◽

Vol 62 (1-2) ◽

pp. 101-112 ◽

Author(s):

M. S. Ismail

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Cubic Spline ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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