摘要
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，严格求解了双曲型ＰｓｃｈｌＴｅｌｅｒ分子势Ｓｃｈｒｄｉｎｇｅｒ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ＰｓｃｈｌＴｅｌｅｒ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．
We present a new potential function with an exactly solvable Schrdinger equation. At the same time, we propose a new variable transformation to show that the hyperbolic Pschl Teller 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 Pschl Teller 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.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
1996年第12期1953-1959,共7页
Acta Physica Sinica
基金
高等学校博士学科点基金
