The Riccati–Padé quantization method for one-dimensional quantum-mechanical models

Abstract

We improve on a previously developed method for the calculation of accurate eigenvalues and eigenfunctions of separable models in quantum mechanics. It consists of the approximation of the logarithmic derivative of the eigenfunction by means of a rational function or Padé approximant. Here we modify the approach by the separation of the function just mentioned into its odd and even parts, thus making the procedure more efficient for treating asymmetric one-dimensional potentials. We obtain the ground-state eigenvalue of anharmonic oscillators with one and two wells and the lowest resonances of anharmonic oscillators that support only continuum states.