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Within the framework of adiabatic approximation, the energy levels and direct interband light absorption in a strongly prolated ellipsoidal quantum dot are studied. Analytical expressions for the particle energy spectrum and absorption threshold frequencies in three regimes of quantization are obtained. Selection rules for quantum transitions are revealed. Absorption edge and absorption coefficient for three regimes of size quantization (SQ) are also considered. To facilitate the comparison of obtained results with the probable experimental data, size dispersion distribution of growing quantum dots by the small semiaxe in the regimes of strong and weak SQ by two experimentally realizing distribution functions have been taken into account. Distribution functions of Lifshits-Slezov and Gaussian have been considered.

Densities of persistent orbital and spin magnetic moment currents of an electron in a cylindrical nanolayer in the presence of external axial magnetic field are considered. For the mentioned current densities analytical expressions are obtained. The conditions when in the system only spin magnetic moment current is present are defined. Dependencies of orbital and spin magnetic moment currents on geometrical parameters of nanolayer are derived. It is shown that in the case of layered geometry the dependence of spin magnetic moment current on radial coordinate has a non-monotonic behavior. This is the peculiarity of layered geometry of nanostructure and it is due to the behavior of wave function of the system along the radial direction. Dependent on the directions of the field and orbital rotation of the electron there are defined values of radial coordinates when the orbital current disappears. The transition to the case of cylindrical quantum dot is discussed as well., Comment: 9 pages, 11 figures

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size making use of the total sets of exact and adiabatic quantum numbers in appropriate analytic approximations.

In this article it is shown that, Sommerfeld's coefficients for excitonic transitions in quantum wells are determined only with the principle quantum number within the framework of two-dimensional Coulomb potential. This is a consequence of hidden symmetry of two-dimensional Coulomb problem, conditioned by the existence of two-dimensional analog of the Runge-Lentz vector. For the narrow gap semiconductor quantum well with the non-parabolic dispersion law of electron and hole in the two-band Kane model it is shown that two-dimensional excitonic states are described in the frames of an analog of Klein-Gordon equation with the two-dimensional Coulomb potential. The non-stability of the ground state of the two-dimensional Kane's exciton is show., Comment: 11 pages, grant number added