Computation of relativistic terms in a spherical quantum dot

We studied a hydrogenic impurity located at the center of a spherical quantum dot with an infinite spherical confining potential and calculated energy levels and wavefunctions using Quantum Genetic Algorithm(QGA) and Hartree–Fock Roothaan (HFR) method. In addition, we investigated the first-order relativistic terms such as the relativistic correction to the kinetic energy, Darwin and spin–orbit interaction term. These terms were calculated using the first-order perturbation theory. The electronic charge density for the Darwin term was carried out from a global operator defined by Hiller, Sucher and Feinberg. The results revealed that the relativistic corrections are important in small dot radii and they should not be neglected to improve the accuracy of calculations.