A solvable model of hydrogenic impurities in quantum dots

Abstract

A solvable model is developed for electronic structure calculations of shallow hydrogenic impurities in two-dimensional quantum dots. We replace the actual Coulomb interaction (local potential) between the electron and the hydrogenic impurity by a projective operator (non-local separable potential) to determine the resulting electronic states in closed form. It is shown that non-local separable potentials may be used to accurately calculate the energy shift of the electronic levels as a function of the size of the quantum dot and the impurity position.