Model of excitations in quantum dots based on quantum mechanics in spaces of constant curvature

The model for the description of the spectra of electrons, holes, and excitons confined in semiconductor quantum dots is proposed. The model is based on quantum mechanics, in spaces of constant curvature. It is shown that the model allows the interpretation in terms of the particle motion in ordinary three-dimensional space with coordinate-dependent effective mass. The comparison with the experiment is carried out for CdSe and InAs quantum dots.