Understanding the analysis of wave function

Abstract

We obtained the order $\ddot{I}$ and the type $\ddot{I}ƒ$ of wave function with power-law potentials, and found that the order and the type are compatible with the condition $|\ddot{I}ƒ|\ddot{I}=\sqrt{v_m}$ except to $m=-2$. At the same time, we ansatz that the wave function satisfaction relation $\ddot{I}ˆ(r)=f(r)\exp [g(r)]$, where $f(r),g(r)$ are polynomials, and the power of $g(r)$ is no more than the order $\ddot{I}$.