Accurate boundary treatment for transient Schrödinger equation under polar coordinates

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• 作者：Lei Bian^a ; ^{bianlei@pku.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Songsong Ji^a ; ^{songsong.0211@163.com" class="auth_mail" title="E-mail the corresponding author} ; Gang Pang^b ; ^{1517191281@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Shaoqiang Tang^a ; ^{maotang@pku.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Two-dimensional Schrö ; dinger equation ; Polar coordinates ; Boundary conditions
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：71
• 期：2
• 页码：479-488
• 全文大小：1241 K

文摘

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.