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^*

^*Corresponding author for this work

Peking University
IAPCM

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	479-488
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	71
Issue number	2
DOIs	https://doi.org/10.1016/j.camwa.2015.12.018
State	Published - 1 Jan 2016
Externally published	Yes

Keywords

Boundary conditions
Polar coordinates
Two-dimensional Schrödinger equation

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10.1016/j.camwa.2015.12.018

Cite this

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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",

year = "2016",

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doi = "10.1016/j.camwa.2015.12.018",

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AU - Bian, Lei

AU - Ji, Songsong

AU - Pang, Gang

AU - Tang, Shaoqiang

PY - 2016/1/1

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

Abstract

Keywords

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