The Exact Solution to the Schrödinger Equation with the Octic Potential

Abstract

The Schrödinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schrödinger equation for the radial wave function through a simple transformation. As an example, applying an $ansatz$ to the eigenfunctions, we then arrive at an exact closed form solution to the modified two-dimensional Schrödinger equation with the octic potential, $V(r)=a{r}^2-b{r}^4+c{r}^6-d{r}^4+e{r}^{10}$.

Latex file 9 pages and submit to J. P. A