Accurate eigenvalues of the Schrödinger equation with the potential $V\left(r\right)=V_0{r}^{\alpha }$

We calculate accurate eigenvalues of the Schrödinger equation with the potential $V\left(r\right)=V_0{r}^{\alpha }$, α ≥ −1, V ₀ α > 0. We resort to the Riccati-Padé method that is based on a rational approximation to the logarithmic derivative of the wavefunction. This approach applies when α is a rational number. (paper)