Accurate eigenvalues of the Schr\"odinger equation with the potential $V(r)=V_{0}r^{\alpha}$

Abstract

We calculate accurate eigenvalues of the Schr\"odinger equation with the potential $V(r)=V_{0}r^{\alpha}$, $\alpha \geq -1$, $V_{0}\alpha >0$. 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.