Calculation of bound states and resonances in perturbed Coulomb models

TL;DR

This paper employs the Riccati-Padé method to accurately compute bound states and resonances in perturbed Coulomb models, offering a reliable numerical approach for quantum systems with Coulomb interactions.

Contribution

It introduces the Riccati-Padé method for precise calculation of eigenvalues in perturbed Coulomb models, enhancing numerical accuracy over existing techniques.

Findings

Accurate bound state energies obtained for perturbed Coulomb models.

Resonance positions identified with high precision.

Convergence of the method demonstrated through numerical results.

Abstract

We calculate accurate bound states and resonances of two interesting perturbed Coulomb models by means of the Riccati-Pad\'{e} method. This approach is based on a rational approximation to a modified logarithmic derivative of the eigenfunction and produces sequences of roots of Hankel determinants that converge towards the eigenvalues of the equation.