Matrix methods for the numerical solution of relativistic wave equations

An efficient new method is presented for the solution of eigenvalue problems that involve nonlocal operators of the type that appear in the solution of relativistic wave equations. The method, which has wider utility, allows very accurate results to be obtained with small matrix approximations to the eigenvalue equation. The method is illustrated for the equation [2(−∇2+m2)1/2+V(r)−M]ψ=0.