We investigate the application of the Sturmian basis set to relativistic atomic structure calculations. We propose a simple implementation of this approach and demonstrate its ability to provide various quantities for hydrogenlike ions, including binding energies, static dipole polarizability, the $g$ factor, hyperfine splitting, and nuclear magnetic shielding. Finally, we calculate the all-order (Wichmann-Kroll) vacuum-polarization charge density, which was a challenge for the finite-basis-set approach until recently. We present a comparison of the obtained results with previously published numerical and analytical calculations. All calculations are performed with nuclei of a finite size and can, in principle, be extended to arbitrary binding potentials.

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• Atomic spectra
• Bound states
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Ions