最弱受约束电子势模型的径向波函数的两类递推关系

应用简单的方法———Laplace变换法来求最弱受约束电子势模型(WBEPM势)的径向Schrdinger方程.通过这种方法使得两阶微分方程变为一阶微分方程,这样可以直接运用积分得到WBEPM势束缚态能量方程和归一化的波函数,所得结果与文献一致.更重要的是用Laplace变换得到径向波函数的两类新的递推关系.这种递推关系是有效主量子数和角量子数之间关系,在计算原子和分子跃迁几率时有着广泛的应用.

Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000

A simplified method, Laplace transformation, is used to discuss the radial Schrodinger equation with the weakest bound electron potential model (WBEPM). Through using such method, the second-order differential equation is reduced to a first-order differential equation and the exact bound state solutions including energy spectrum and normalized wave functions are obtained by making use of the integral. The results agree with those obtained by Zheng. It is most important that the two kinds of new recursion relations of radial wave functions are derived by the same method. These new recursion relations are the relations between the effective principal and angular-momentum quantum numbers, and are comprehensive in application to the calculations of transition probabilities in atomic and molecular physics.