Least squares B-spline solutions of the radial Dirac equation in the continuum Original Research Article

The B-spline least-squares approach for the determination of the continuum wavefunctions, which proves to be very accurate and numerically stable in the non-relativistic case has been generalized to the relativistic case. The least-squares scheme has been tested in the free-particle and Coulomb problems. Expression of relativistic Coulomb functions in terms of the corresponding non relativistic ones is spelled out in detail and employed for testing the spline solutions. The convergence properties of the algorithm with respect to the B-spline order and the radial grid are also analyzed.