径向积分的解析计算

计算物理 ›› 1987, Vol. 4 ›› Issue (3): 284-298.

径向积分的解析计算

蔡崇海¹, 王思问²

1. 天津南开大学;
2. 西安西北大学

收稿日期:1986-10-05 修回日期:1987-06-01 出版日期:1987-09-25 发布日期:1987-09-25

ANALYTICAL CALCULATION OF THE RADIAL INTEGRALS

Cai Chong-hai¹, Wang Si-wen²

1. Nankai University, Tianjin;
2. Xibei University, Xian

Received:1986-10-05 Revised:1987-06-01 Online:1987-09-25 Published:1987-09-25

摘要/Abstract

摘要： 本文阐明的方法能方便地求出径向积分ⁿ₁^l₁F_Lⁿ₂^l₂(q)≡∫₀^∞> (R_n₁^l₁(αr)jL(Kr)R_n₂^l₂(αr)r²dr(q≡(K)/(α))的解析表达式。文中给出了L=0,1,2情况下各个径向积分的解析式,同时还以多重求和的形式络出了对各种量子数L,n₁,l₁,n₂,l₂适用的径向积分表达式。

关键词: 径向积分, 三维谐振子场, 径向波函数, 球贝塞尔函数

Abstract: In this work we describe a method from which one can conveniently derive the analytical expression of the radial integralsⁿ₁^l₁F_Lⁿ₂^l₂(q)≡∫₀^∞ (R_n₁^l₁·(αr)jL(Kr)R_n₂^l₂(αr)r²dr(q≡(K)/(α)). We also give the analytical expressions of for ⁿ₁^l₁F_Lⁿ₂^l₂ L=0,1,2, and a general form of the radial integrals for all L,n₁,l₁,n₂,l₂ expressed by multi-sum.

蔡崇海, 王思问. 径向积分的解析计算[J]. 计算物理, 1987, 4(3): 284-298.

Cai Chong-hai, Wang Si-wen. ANALYTICAL CALCULATION OF THE RADIAL INTEGRALS[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1987, 4(3): 284-298.