Accurate boundary treatment for transient Schrödinger equation under polar coordinates

Lei Bian; Songsong Ji; Gang Pang; Shaoqiang Tang

doi:10.1016/j.camwa.2015.12.018

Accurate boundary treatment for transient Schrödinger equation under polar coordinates

Lei Bian
, Songsong Ji
, Gang Pang
, Shaoqiang Tang^*

^*此作品的通讯作者

Peking University
IAPCM

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

A new local boundary condition is designed for the two dimensional Schrödinger equation under polar coordinates. Based on an approximate linear relation among the kernel functions for a free one-dimensional Schrödinger equation of a new variable, it takes a simple form of ordinary differential equation that relates the neighboring grid points. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment.

源语言	英语
页（从-至）	479-488
页数	10
期刊	Computers and Mathematics with Applications
卷	71
期	2
DOI	https://doi.org/10.1016/j.camwa.2015.12.018
出版状态	已出版 - 1 1月 2016
已对外发布	是

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10.1016/j.camwa.2015.12.018

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title = "Accurate boundary treatment for transient Schr{\"o}dinger equation under polar coordinates",

abstract = "A new local boundary condition is designed for the two dimensional Schr{\"o}dinger equation under polar coordinates. Based on an approximate linear relation among the kernel functions for a free one-dimensional Schr{\"o}dinger equation of a new variable, it takes a simple form of ordinary differential equation that relates the neighboring grid points. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment.",

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author = "Lei Bian and Songsong Ji and Gang Pang and Shaoqiang Tang",

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T1 - Accurate boundary treatment for transient Schrödinger equation under polar coordinates

AU - Bian, Lei

AU - Ji, Songsong

AU - Pang, Gang

AU - Tang, Shaoqiang

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Y1 - 2016/1/1

N2 - A new local boundary condition is designed for the two dimensional Schrödinger equation under polar coordinates. Based on an approximate linear relation among the kernel functions for a free one-dimensional Schrödinger equation of a new variable, it takes a simple form of ordinary differential equation that relates the neighboring grid points. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment.

AB - A new local boundary condition is designed for the two dimensional Schrödinger equation under polar coordinates. Based on an approximate linear relation among the kernel functions for a free one-dimensional Schrödinger equation of a new variable, it takes a simple form of ordinary differential equation that relates the neighboring grid points. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment.

KW - Boundary conditions

KW - Polar coordinates

KW - Two-dimensional Schrödinger equation

UR - https://www.scopus.com/pages/publications/84960804787

U2 - 10.1016/j.camwa.2015.12.018

DO - 10.1016/j.camwa.2015.12.018

M3 - 文章

AN - SCOPUS:84960804787

SN - 0898-1221

VL - 71

SP - 479

EP - 488

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -

Accurate boundary treatment for transient Schrödinger equation under polar coordinates

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