Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials
For researchers in relativistic quantum mechanics, this method offers a reliable alternative to variational approaches that suffer from spectral pollution, though it is domain-specific.
The paper presents a non-variational method for computing eigenstates of Dirac operators with radially symmetric potentials that avoids spectral pollution and provides two-sided eigenvalue estimates with explicit error bounds. Numerical experiments demonstrate convergence rates.
We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie on the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-side estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method as well as illustrate our results with various numerical experiments.