修正Poschl-Teller势的Schrdinger方程束缚态的精确解

EXACT SOLUTIONS OF BOUND STATES OF THESCHRODINGER EQUATION WITH MODIFIEDPOSCHL-ELLER POTENTIAL

将修正P(?)schl-Teller势的Scbr(?)dinger方程作自变量双曲函数变换,使其转化为普遍的associated-Legendre方程.用级数法解此方程,得到了用普遍的associated-Legendre多项式表示的修正Poschl-Teller势的束缚态的归一化波函数.文献[1—5]中的有关结果都作为特例包含在本文的一般结论之中.

Using a hyperbolic function transformation, the Schrodinger equation with modified Poschl-Teller potential is transformed into a universal associated-Legendre equation. The bound state eigenfunctions of modified Poschl-Teller potential expressed in terms of universal associaced-Legendre polynomials ean be obtained as this equation is solved by using series expansion method. The relevant results in are contained in more general conclusions of this paper as special cases.