Airy函数乘积的积分

本文提出对∫xⁿA^(p)B^(q)dx型不定积分普遍方法,其中A,B都是含有参变量λ的Airy方程y″=(λ+x)y的解,p,q是微分阶数,n是非负整数。当p,q≤1,A与B所含的参数不相同时,本文导出了上述积分普遍公式。当A=B时,又提出了与Albright完全不相同的求积方法。作为它的应用,本文讨论了处于三角势阱中电子的波函数正交归一问题,并计算了势阱中能级间的跃迁几率。 关键词：

INTEGRALS OF PRODUCTS OF AIRY FUNCTIONS

General methods of calculating indefinite integrals of the type ∫xⁿA^(p)B^(q)dx are pre-sented, where A and B are solutions of the Airy equition y" = (λ + x)y with the para-meterλ, p, q are the order of differential, n is a non-negative integer. General formulae of this type of integrals is given for corresponding p, q ≤1 and functions A, B with dif-ferent parameters. For A=B a method of integration is also obtained, which is quite dif-ferent from that of Albright. As an application, these formulae of integrals are applied to the problem of the orthonormalization of the wave functions of an electron in a triangular potential well, and the transition probabilities between the energy-levels are obtained.