Bound and Resonance States of Singular Potentials Using the Lagrange-Laguerre mesh Method

In this work, we illustrate the numerical accuracy and stability of the Lagrange-Laguerre mesh method for calculating both bound and resonance states associated with few highly singular central potential problems. To test the accuracy of our numerical approach we first use a test central potential which has well defined s-wave resonances used usually as a benchmark in the literature. Then we considered a hyperbolic singular potential which has a rich structure and allows for both resonances and bound states depending on the values of the potential parameters. We also displayed the spectral phase diagram of this potential which exposes the different parameter space sectors that allow for bound and/or resonance states which are associated with the energy spectrum of this potential.