求解一维Schrödinger方程的P稳定Obrechkoff两步方法

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (1): 53-58.

求解一维Schrödinger方程的P稳定Obrechkoff两步方法

郝海玲,汪仲诚,邵和助,陈佳奇

（上海大学理学院,上海 200444）

收稿日期:2008-06-04 出版日期:2010-02-28 发布日期:2010-02-28
通讯作者: 汪仲诚(1946～)，男，教授，博士生导师,研究方向为计算物理. E-mail:zc_wang@hotmail.com
基金资助:
上海市教委科研基金资助项目(A.10-0101-06-426）

A P-Stable Two-Step Obrechkoff Method for One-Dimensional Schrödinger Equation

HAO Hai-ling,WANG Zhong-cheng,SHAO He-zhu,CHEN Jia-qi

(College of Sciences, Shanghai University, Shanghai 200444, China)

Received:2008-06-04 Online:2010-02-28 Published:2010-02-28

摘要/Abstract

摘要：

提出一种新的高精度、高效率求解一维Schrödinger方程的Obrechkoff两步方法.通过增加奇数次高阶微商项，大幅度提高了经典Obrechkoff两步递推公式的精度.由求解Morse势束缚态本征值的数值例子表明,在精度和效率上该方法比经典方法求解一维Schrödinger方程有明显的优势.

关键词: Obrechkoff方法;一维Schrödinger方程;P稳定

Abstract:

In this paper, a new kind of P-stable two-step Obrechkoff method for the ultrahighaccurate solution of a onedimensional Schrödinger equation is proposed. Improving Wang’s method, a new P-stable two-step Obrechkoff method by adding odd derivatives of higher-order has been developed. The proposed method is effective but has high local truncation error. By using the new approach, one can obtain solutions of the wellknown one-dimensional Schrödinger equation. Numerical experiments on the well-known Morse potential demonstrate that our method has the advantage over Wang’s both in accuracy and efficiency.

Key words: Obrechkoff method; one-dimensional Schrdinger equation; P-stable

中图分类号:

O 411

郝海玲,汪仲诚,邵和助,陈佳奇. 求解一维Schrödinger方程的P稳定Obrechkoff两步方法[J]. 上海大学学报(自然科学版), 2010, 16(1): 53-58.

HAO Hai-ling,WANG Zhong-cheng,SHAO He-zhu,CHEN Jia-qi. A P-Stable Two-Step Obrechkoff Method for One-Dimensional Schrödinger Equation[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(1): 53-58.