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

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 ◽  
The One

scholarly journals Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

2011 ◽  
Vol 10 (5) ◽  
pp. 1280-1304 ◽  
Author(s):  
Pauline Klein ◽  
Xavier Antoine ◽  
Christophe Besse ◽  
Matthias Ehrhardt
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Absorbing Boundary Conditions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
Nonlinear Potential ◽  
Linear And Nonlinear ◽  
The One

AbstractWe propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.

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