连续态数值波函数归一化的近似计算及TRK求和中余项的积分处理

计算物理 ›› 2006, Vol. 23 ›› Issue (1): 115-119.

连续态数值波函数归一化的近似计算及TRK求和中余项的积分处理

曹伟, 朱云霞, 陆慧, 贺黎明

华东理工大学物理系, 上海 200237

收稿日期:2004-08-16 修回日期:2005-01-17 出版日期:2006-01-25 发布日期:2006-01-25
作者简介:曹伟(1982-),男,江苏,硕士生,主要从事计算原子分子物理的研究.
基金资助:
国家自然科学基金(10074014)资助项目

Approximate Normalization of Numeric Continuum State Wave Functions and Integral Processing of Residues in TRK Sums

CAO Wei, ZHU Yun-xia, LU Hui, HE Li-ming

Department of Physics, East China University of Science and Technology, Shanghai 200237, China

Received:2004-08-16 Revised:2005-01-17 Online:2006-01-25 Published:2006-01-25

摘要/Abstract

摘要： 采用改进的Numerov格式,对连续态波函数及其归一化问题作了细致的计算.指出了Cowan在ε→0时状态波函数的归一化中存在的问题,给出了更加准确、有效的归一化计算目的.为了检验这一算法,计算了氢原子各状态(l=0~3)下的Thomas-Reiche-Kuhn(TRK)和.利用最小二乘法,给出了TRK求和中无穷项的渐近函数形式,并由此采用积分目的得到了余项的近似计算结果.

关键词: 连续态, 归一化, TRK和定则, 积分处理

Abstract: With an improved Numerov algorithm, continuum state wave functions and its normalization are investigated. Cowan' s normalization is discussed and a more precise and effective calculation is offered. We calculate the Thomas-Reiche-Kuhn(TRK) sum of several hydrogen atomic states (l=0~3). The least-squared method is used to generate infinite asymptotical forms of TRK. The residues are approximately calculated with an integral processing.

Key words: continuum state, normalization, TRK sum rules, integral processing

中图分类号:

O562

曹伟, 朱云霞, 陆慧, 贺黎明. 连续态数值波函数归一化的近似计算及TRK求和中余项的积分处理[J]. 计算物理, 2006, 23(1): 115-119.

CAO Wei, ZHU Yun-xia, LU Hui, HE Li-ming. Approximate Normalization of Numeric Continuum State Wave Functions and Integral Processing of Residues in TRK Sums[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 23(1): 115-119.

[1]	耿方志, 彭世蕤, 秦开兵, 潘英锋, 孙宏伟. 一种新的计算复杂目标电磁散射的MoM-SBR/PO混合法[J]. 计算物理, 2010, 27(2): 269-273.
[2]	周忠源, 吴承埙, 丁培柱. 关于波函数模方逐步归一化修正的注记[J]. 计算物理, 1997, 14(S1): 431-432.
[3]	徐启阳, 宋一新, 王新兵, 杨克成, 朱晓, 谢明杰, 李再光. 平板宽波导光场分布及极化模[J]. 计算物理, 1996, 13(1): 79-86.