Exact Solutions of the two-dimensional Schrödinger equation with certain central potentials

Shi-Hai Dong

By applying an ansatz to the eigenfunction, an exact closed form solution of the Schrödinger equation in 2D is obtained with the potentials, $V(r)=a{r}^2+b{r}^4+c{r}^6$, $V(r)=ar+br^2+cr…