Klein-Gordon equationon a Lagrange mesh.

Abstract

The Lagrange-mesh method is an approximate variational method which provides accurate solutions of the Schrödinger equationfor bound-state and scattering few-body problems. The stationary Klein-Gordon equationdepends quadratically on the energy. For a central potential, it is solved on a Lagrange-Laguerre mesh by iteration. Results are tested with the Coulomb potential for which exact solutions are available. A high accuracy is obtained with a rather small number of mesh points. For various potentials and levels, few iterations provide accurate energies and mean values in short computer times. Analytical expressions of the wave functions are available.