A comparison of the eigenstates of a hydrogenic impurity in spherical and parabolic quantum dots

In previous papers we calculated the energy spectra of a hydrogen impurity located at the center of spherical and parabolic quantum dots. In this work, a comparison of the eigenstates of a hydrogenic impurity in spherical and parabolic quantum dots is discussed in detail. Moreover, the Stark effect on the parabolic quantum dots is investigated. Our calculated results reveal that for both spherical and parabolic quantum dots, the eigenenergies are just like those of a free-space hydrogenic atom, when the dot size is extremely small. On the other hand, the eigenenergies are also like those of a free-space hydrogenic atom when the dot size is extremely large, except that they are shifted by the confining potential. When the dot size is between these two extreme situations, the energy level splitting and degeneracy of the energy levels are quite different for these two cases. The theoretical results show that the energy plateau of the parabolic quantum dot is not obvious when compared to that of the spherical quantum dot.