中国物理B ›› 2005, Vol. 14 ›› Issue (12): 2402-2406.doi: 10.1088/1009-1963/14/12/005

• GENERAL • 上一篇    下一篇

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

陆军, 钱卉仙, 李良梅, 柳凤伶   

  1. College of Arts and Sciences of Beijing Union University, Beijing 100083, China
  • 收稿日期:2005-04-22 修回日期:2005-08-09 出版日期:2005-12-20 发布日期:2005-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 90403028).

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

Lu Jun (陆军), Qian Hui-Xian (钱卉仙), Li Liang-Mei (李良梅), Liu Feng-Ling (柳凤伶)   

  1. College of Arts and Sciences of Beijing Union University, Beijing 100083, China
  • Received:2005-04-22 Revised:2005-08-09 Online:2005-12-20 Published:2005-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 90403028).

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摘要： The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.

Abstract: The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.

Key words: diatomic molecule, hyperbolic potential, matrix elements

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
03.65.Db (Functional analytical methods) 02.10.Ud (Linear algebra)