Electronic states in quantum dots with ellipsoidal symmetry

In the framework of perturbation theory and for any limiting potential with ellipsoidal symmetry energy states of electron in weakly oblate (prolate) ellipsoidal quantum dot has been investigated. Analytical expressions for particle energy spectrum have been obtained taking into account that electron effective masses are different in medium and in quantum dot. Obtained results were applied for the case of rectangular quantum well of finite height. The investigation of energy level dependence on geometrical parameters of quantum dot was performed. In particular, within the first order of perturbation theory it has been shown, that the dependence of energy correction on reduced radius of quantum dot has a maximum.