Accurate boundary treatment for time-dependent 3D Schrodinger equation under Spherical coordinates

被引：1

作者：

Zhang, Linfeng ^{[1
,2
]}

Jia, Hongfei ^{[1
]}

Bian, Lei ^{[1
,3
]}

Ran, Bin ^{[2
]}

机构：

[1] Jilin Univ, Sch Transportat, Changchun 130012, Peoples R China

[2] Univ Wisconsin, 1212 Engn Hall,1415 Engn Dr, Madison, WI 53706 USA

[3] Travelsky Mobile Technol Ltd, Beijing 100087, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MODERN PHYSICS C | 2020年 / 31卷 / 01期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Three-dimensional Schrodinger equation; spherical coordinates; boundary conditions; NUMERICAL-SOLUTION; TRANSPARENT; SCHEMES;

D O I：

10.1142/S0129183120500151

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We propose a novel local boundary condition for three-dimensional Schrodinger equation under spherical coordinates. It is based on the approximate linear relationship among the Bessel functions from a free one-dimensional Schrodinger equation. With a variable transform, the novel boundary condition is a simple form of some ordinary differential equations, which relate the grid point near the numerical boundaries. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary conditions.

引用

页数：13

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