N维各向同性谐振子Schrdinger方程束缚态解及二类递推关系

Bound State Solutions of the Schrdinger Equation with the N-Dimensional Isotropic Harmonic Oscillator and Two Kinds of Recursion Relations

用Laplace变换把二阶N维各向同性谐振子的径向Schr dinger微分方程退化为一阶微分方程,然后用直接积分法求出一阶微分方程的解.用波函数的单值性得到束缚态能谱.用级数展开,再进行Laplace逆变换,得到其本征函数.并给出了径向波函数关于径向量子数'n'和角量子数'l'的二类递推关系.

The second-order N-dimensional radial Schrdinger differential equation with the isotropic harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform, and then, its solutions are directly obtained by means of making use of an integral. The energy spectrum is derived from the condition single-valued of the wave functions. And then to get the required eigenfunctions by apply the expansions of series and inverse Laplace transform. In addition, two kinds of recursion relations of radial wave functions given the form of 'n' and 'l' quantum numbers are also derived.