Regularization of singularities in Lagrange-mesh calculations

The authors propose a regularization technique which allows Lagrange-mesh calculations to retain their accuracy, efficiency and simplicity when the Hamiltonian is singular at finite distance. Compact analytical expressions of kinetic-energy matrix elements are an essential ingredient of the method. The authors present general procedures for deriving them. Their approach is tested on the hydrogen atom and the squared orbital-momentum operator. They demonstrate its accuracy on the non-separable problem of the hydrogen atom in a magnetic field. This method opens the way to numerous new applications of Lagrange-mesh calculations in atomic and molecular physics.