Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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Bifurcation structures and dominant modes near relative equilibria in the one-dimensional discrete nonlinear Schrödinger equation

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2009.01.001 ◽

2009 ◽

Vol 238 (6) ◽

pp. 687-698 ◽

Cited By ~ 11

Author(s):

C.L. Pando L. ◽

E.J. Doedel

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Relative Equilibria ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

The One ◽

Bifurcation Structures

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A Collective Coordinate Approach to the One-Dimensional Nonlinear Schrödinger Equation with Spatial Periodic Potentials

NATO ASI Series - Future Directions of Nonlinear Dynamics in Physical and Biological Systems ◽

10.1007/978-1-4899-1609-9_14 ◽

1993 ◽

pp. 85-96

Author(s):

A. R. Bishop ◽

Rainer Scharf

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Periodic Potentials ◽

Collective Coordinate ◽

The One

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The One-Dimensional Stationary Schrödinger Equation

Basic Concepts in Computational Physics ◽

10.1007/978-3-319-02435-6_10 ◽

2013 ◽

pp. 131-146

Author(s):

Benjamin A. Stickler ◽

Ewald Schachinger

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

The One

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New Method for Rapid Numerical Solution of the One-Dimensional Schrödinger Equation

Physical Review Letters ◽

10.1103/physrevlett.29.1350 ◽

1972 ◽

Vol 29 (19) ◽

pp. 1350-1353 ◽

Cited By ~ 15

Author(s):

William I. Newman ◽

Walter R. Thorson

Keyword(s):

Schrödinger Equation ◽

Numerical Solution ◽

Schrodinger Equation ◽

New Method ◽

One Dimensional ◽

The One

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Stability and Error Analysis for a Second-Order Fast Approximation of the One-dimensional Schrödinger Equation Under Absorbing Boundary Conditions

SIAM Journal on Scientific Computing ◽

10.1137/17m1162111 ◽

2018 ◽

Vol 40 (6) ◽

pp. A4083-A4104 ◽

Cited By ~ 2

Author(s):

Buyang Li ◽

Jiwei Zhang ◽

Chunxiong Zheng

Keyword(s):

Schrödinger Equation ◽

Error Analysis ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Absorbing Boundary Conditions ◽

Second Order ◽

Absorbing Boundary ◽

One Dimensional ◽

The One ◽

Stability And Error Analysis

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On Asymptotic properties of the one-dimensional Schrödinger equation

Complex Analysis and Related Topics ◽

10.1007/978-3-0348-8698-7_2 ◽

2000 ◽

pp. 15-19

Author(s):

Irina V. Astashova

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Asymptotic Properties ◽

One Dimensional ◽

The One

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Exact Solution of the One-Dimensional Schrödinger Equation withδ-Function Potentials of Arbitrary Position and Strength

Physical Review B ◽

10.1103/physrevb.5.556 ◽

1972 ◽

Vol 5 (2) ◽

pp. 556-565 ◽

Cited By ~ 31

Author(s):

John F. Reading ◽

James L. Sigel

Keyword(s):

Exact Solution ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

One Dimensional ◽

Arbitrary Position ◽

The One

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The one-dimensional Schrödinger equation and a periodic potential

Czechoslovak Journal of Physics ◽

10.1007/bf01599671 ◽

1987 ◽

Vol 37 (11) ◽

pp. 1209-1223 ◽

Cited By ~ 2

Author(s):

L. Trlifaj

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Potential ◽

One Dimensional ◽

The One

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