Accurate eigenvalues of the Schr\"odinger equation with the potential $V(r)=V_0{r}^{\alpha }$

We calculate accurate eigenvalues of the Schr"odinger equation with the potential $V(r)=V_0{r}^{\alpha }$, $\alpha \ge -1$, $V_0\alpha >0$. We resort to the Riccati-Pad'e method that is based on a rational approximation to the logarithmic derivative of the wavefunction. This approach applies when $\alpha$ is a rational number.