Efficient representation of nonreflecting boundary conditions for the time-dependent Schrödinger equation in two dimensions

Shidong Jiang; Leslie Greengard

doi:10.1002/cpa.20200

Efficient representation of nonreflecting boundary conditions for the time-dependent Schrödinger equation in two dimensions

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.20200 ◽

2007 ◽

Vol 61 (2) ◽

pp. 261-288 ◽

Cited By ~ 31

Author(s):

Shidong Jiang ◽

Leslie Greengard

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Two Dimensions ◽

Time Dependent ◽

Nonreflecting Boundary Conditions ◽

Efficient Representation

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Numerical implementation of absorbing and injecting boundary conditions for the time-dependent Schrödinger equation

Physical Review B ◽

10.1103/physrevb.51.2082 ◽

1995 ◽

Vol 51 (4) ◽

pp. 2082-2086 ◽

Cited By ~ 4

Author(s):

M. Cemal Yalabik ◽

M. İhsan Ecemiş

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Time Dependent ◽

Numerical Implementation

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Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation

Lecture Notes in Computational Science and Engineering - Numerical Mathematics and Advanced Applications - ENUMATH 2013 ◽

10.1007/978-3-319-10705-9_20 ◽

2014 ◽

pp. 203-211 ◽

Cited By ~ 1

Author(s):

Alexander Zlotnik ◽

Bernard Ducomet ◽

Ilya Zlotnik ◽

Alla Romanova

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Difference Schemes ◽

Time Dependent ◽

Finite Difference Schemes ◽

Transparent Boundary Conditions

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Approximation and Fast Calculation of Non-local Boundary Conditions for the Time-dependent Schrödinger Equation

Lecture Notes in Computational Science and Engineering - Domain Decomposition Methods in Science and Engineering ◽

10.1007/3-540-26825-1_10 ◽

2005 ◽

pp. 141-148 ◽

Cited By ~ 2

Author(s):

Anton Arnold ◽

Matthias Ehrhardt ◽

Ivan Sofronov

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Time Dependent ◽

Fast Calculation ◽

Local Boundary ◽

Non Local

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Radiation boundary conditions for the numerical solution of the three-dimensional time-dependent Schrödinger equation with a localized interaction

Physical Review E ◽

10.1103/physreve.79.056709 ◽

2009 ◽

Vol 79 (5) ◽

Cited By ~ 6

Author(s):

M. Heinen ◽

H.-J. Kull

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Numerical Solution ◽

Schrodinger Equation ◽

Three Dimensional ◽

Time Dependent ◽

Radiation Boundary Conditions ◽

Radiation Boundary

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Stability of a symmetric finite-difference scheme with approximate transparent boundary conditions for the time-dependent Schrödinger equation

Doklady Mathematics ◽

10.1134/s1064562407020214 ◽

2007 ◽

Vol 75 (2) ◽

pp. 260-265

Author(s):

A. A. Zlotnik ◽

B. Ducomet

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Schrodinger Equation ◽

Time Dependent ◽

Transparent Boundary Conditions

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Numerical solutions of the time-dependent Schrödinger equation in two dimensions

Physical Review E ◽

10.1103/physreve.95.023310 ◽

2017 ◽

Vol 95 (2) ◽

Cited By ~ 3

Author(s):

Wytse van Dijk ◽

Trevor Vanderwoerd ◽

Sjirk-Jan Prins

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Numerical Solutions ◽

Two Dimensions ◽

Time Dependent

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Time-dependent schrödinger equation with Markovian outgoing wave boundary conditions: Applications to quantum tunneling dynamics and photoionization

International Journal of Quantum Chemistry ◽

10.1002/qua.24005 ◽

2012 ◽

Vol 113 (1) ◽

pp. 39-44 ◽

Cited By ~ 7

Author(s):

Chia-Chun Chou ◽

Robert E. Wyatt

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Quantum Tunneling ◽

Schrodinger Equation ◽

Time Dependent ◽

Outgoing Wave ◽

Tunneling Dynamics ◽

Wave Boundary

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Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

Physics Letters A ◽

10.1016/j.physleta.2018.09.043 ◽

2018 ◽

Vol 382 (46) ◽

pp. 3347-3354 ◽

Cited By ~ 3

Author(s):

A. Matzkin ◽

S.V. Mousavi ◽

M. Waegell

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Time Dependent ◽

Local Causality

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Exact boundary conditions at finite distance for the time-dependent Schrödinger equation

Physical Review A ◽

10.1103/physreva.57.3245 ◽

1998 ◽

Vol 57 (5) ◽

pp. 3245-3255 ◽

Cited By ~ 23

Author(s):

M. Mangin-Brinet ◽

J. Carbonell ◽

C. Gignoux

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Time Dependent ◽

Exact Boundary ◽

Finite Distance

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Integral boundary conditions for the time-dependent Schrödinger equation: Superposition of the laser field and a long-range atomic potential

Physical Review A ◽

10.1103/physreva.62.015401 ◽

2000 ◽

Vol 62 (1) ◽

Cited By ~ 7

Author(s):

A. M. Ermolaev ◽

A. V. Selin

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Long Range ◽

Laser Field ◽

Schrodinger Equation ◽

Integral Boundary Conditions ◽

Time Dependent ◽

Integral Boundary ◽

Atomic Potential

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