Accurate eigenvalues of the Schrödinger equation with the potential V(r)=V0rα

Abstract

We calculate accurate eigenvalues of the Schrödinger equation with the potential V(r)=V0rα, 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.