Electronic structure and relativistic terms of one-electron spherical quantum dot

We calculated the energy eigenvalues and eigenfunctions of the ground and excited states of a hydrogenic impurity located at the center of a spherical quantum dot using the Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothaan (HFR) method. In addition, we carried out the relativistic effects such as the relativistic correction to the kinetic energy, spin–orbit and Darwin terms by using the perturbation method. The electronic charge density for the Darwin term is computed from the Hiller, Sucher and Feinberg formulation instead of the traditional delta function operator. The results show that impurity, dot radius and confining potential have a great influence on the relativistic effects. In addition, as the absolute value of confining potential increases, the peak values of relativistic corrections increase and move toward lower dot radii. ► The electronic structure of a spherical quantum dot with a finite confining potential has been investigated. ► The wavefunctions and the total energy of the quantum dot have been calculated using the Quantum Genetic Algorithm and Hartree–Fock Roothaan method. ► The relativistic energy corrections have been calculated using the first-order perturbation theory.