两个严格可解的双原子分子势函数

提出了一个新的势函数，其Ｓｃｈｒ?ｄｉｎｇｅｒ方程严格可解．同时提出一个新的变量变换关系，严格求解了双曲型Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ分子势Ｓｃｈｒ?ｄｉｎｇｅｒ方程的束缚态．得出的能级公式形式封闭、简单，归一化波函数用超几何级数表达．文献中关于Ｈｕｌｔｈéｎ势和修正Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ势及无反射势的结果都作为特例包含在本文更一般的结论之中．最后，还讨论了本文势函数对双原子分子的实际应用．关键词：

TWO EXACTLY SOLVABLE POTENTIALS FOR DIATOMIC MOLECULES

We present a new potential function with an exactly solvable Ｓｃｈｒ?ｄｉｎｇｅｒ equation. At the same time, we propose a new variable transformation to show that the hyperbolic Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ molecular potential is also exactly solvable. The form of the solutions is not only closed, but also very simple. The normalized wave functions are expressed by the hypergeometric series. All the results of the Hulthéｎ potential and the modified Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ potential as well as the reflectionless potential in the existing literature are contained in the more general conclusions of this paper as special cases. Finally, practical applications of the potentials in this paper to diatomic molecules are discussed.
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