Impurity states in a narrow band gap semiconductor quantum dot with parabolic confinement potential

Impurity states in a narrow band gap semiconductor quantum dot are studied theoretically. The quantum dot confinement potential is approximated by the three-dimensional spherically symmetric parabolic potential. The electron dispersion law is considered within the framework of two-band Kane model. It is shown that the nonparabolicity leads to the Schroedinger equation with the effective oscillatory potential containing terms proportional to 1/r, r, r4. Within the framework of the stationary theory of perturbation the energy corrections due to these terms are calculated.