Stability of a Numerov type finite–difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis

2010 ◽  
Vol 169 (1) ◽  
pp. 84-97 ◽  
Author(s):  
A. A. Zlotnik ◽  
A. V. Lapukhina
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Schrodinger Equation ◽  
Transparent Boundary Conditions ◽  
Nonstationary Schrödinger Equation ◽  
Half Axis

Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Alexander Zlotnik ◽  
Ilya Zlotnik
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Finite Difference Schemes ◽  
Transparent Boundary Conditions ◽  
Space Step ◽  
Half Axis ◽  
Generalized Time

AbstractWe consider the generalized time-dependent Schrödinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a simplified form explicit in space step

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