Handling the Cornell potential within the Lagrange-mesh method in momentum space

Abstract

This work presents an alternative methodology for computing potentials matrix elements within the Lagrange-mesh method in momentum space. The proposed approach extends the range of treatable potentials to include previously inaccessible cases, such as the Coulomb and linear interactions. It enables, in particular, an efficient and accurate treatment of the Cornell potential, which plays an important role in potential models for hadronic physics. The method is validated across a variety of systems, with special attention given to the representation of both momentum and position probability densities.