两个严格可解双原子分子势函数的散射态解与转动修正

THE EXACT SCATTERING SOLUTIONS AND THE ROTA TIONAL MODIFICATIONS FOR TWO EXACTLY SOLVABLE DIATOMIC MOLECULAR POTENTIALS

文献［１］中提出了一个新的势函数，其Ｓｃｈｒｄｉｎｇｅｒ方程严格可解。同时提出一个新的变量变换关系，用超几何级数严格求解了双曲型ＰｓｃｈｌＴｅｌｅｒ分子势Ｓｃｈｒｄｉｎｇｅｒ方程的束缚态。文内进一步讨论这两个势函数Ｓｃｈｒｄｉｎｇｅｒ方程散射态的严格解，并求出了Ｓ波的散射相移。文献中关于修正ＰｓｃｈｌＴｅｌｅｒ势及无反射势散射态的结果均作为特例包含在这篇文章更一般的结论之中。此外还用一个简单的方法考虑了转动能修正。

In Ref, A new diatomic molecular potential is advanced, its Schrdinger equation is exactly solvable. At the same time, a new variable transformation is proposed to show that the Schrdinger equation of the hyperbolic Pschl Teller molecular potential also is exactly solvable by the use of hypergeometric series. In this paper, the discussion is extended to the scattering state solutions of the two potentials and the scattering phase shift of the S wave is obtained. The results on the scattering state of the modefied Pschl Teller potential and the reflection less potential in the existed literature are contained in more general conclusions of this paper as special cases. Otherwise, the rotational energy modifications are considered through a simple method. The specific calculation to the ground state rotational level of HF is done which shows the accuracy is corresponded to the Morse potential. The potentials in this paper are only two potentials found so far that both bound and scatering state Schrdinger equations are exactly sol vable. It is useful to the research of some problem.