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Abstract: We present the theoretical consideration of the states of charge carriers in the HgS quantizing layer of a cylindrical core/layer/shell β-CdS/β-HgS/β-CdS heterostructure in the effective mass approximation within the framework of a simple two-band model. Various ranges of the geometric dimensions of the sample are considered by implementing the corresponding regimes of dimensional quantization for charge carriers in the layer. The electrostatic interaction between the electron and the hole is taken into account for each case, and, depending on the size of the sample, the corresponding values of the ground state energy of the pair are obtained. We also considered interband optical transitions in the sample and photoluminescence in each case. In each case, taking into account the electrostatic interaction leads to a shift in the threshold frequency of interband absorption and luminescence to the short-wavelength region, and the frequency itself is determined by the geometric dimensions of the sample.

In this paper two electronic states in spherical quantum nanolayer are discussed. The Coulomb interaction between the electrons is discussed as perturbation. For confinement potential of the nanolayer the three-dimensional radial analog of Smorodinsky-Winternitz potential is considered. The problem is discussed within the frameworks of Russell-Saunders coupling scheme, thus, the spin-orbit interaction is considered weak. Therefore the eigenfunctions of the system is represented as a multiplication of its coordinate wave function and spin wave function. For this system the analogue of helium atom theory is represented. The eigenfunctions and energy states are obtained for one and two electron cases in the spherical quantum nanolayer. For the spherical nanolayer the dependence of perturbation energy, unperturbed system energy and the total energy for the ground state upon the inner radius is represented when the outer radius is fixed.

Within the framework of adiabatic approximation the energy levels and direct interband light absorption in a strongly prolated ellipsoidal quantum dot are studied. For treatment of the "slow" subsystem modified Pöschl-Teller effective potential is used. It is shown that the low-energy levels of the spectrum are equidistant. Analytical expressions for the particle energy spectrum and absorption threshold frequencies in strong quantization regime are obtained. Selection rules for quantum transitions, absorption edge and absorption coefficient are revealed. Size dispersion distribution of quantum dots by the minor semiaxe by two experimentally realizing distribution, Lifshits-Slezov and Gaussian functions, have been taken into account.

The electronic states and coupling effect in the laterally stacked symmetric and asymmetric quantum-dot-molecules (QDMs) are studied. The formed potential of QDM is approximated with parabolic and modified Pöschel-Teller (MPT) potentials. It is shown that the coupling criterion of quantum dots (QDs) is the energy levels split due to the tunneling effect. In the case of the asymmetric QDM the electron relocalization step-like behavior is revealed, while in the symmetric case it is principally impossible. The obtained results for parabolic and modified Pöschel-Teller potential confinements are compared. The formation of energy levels split for a given range of values of energy (coupling criterion) as a consequence of the finiteness of the confinement potential is revealed for the case of modified Pöschel-Teller potential approximation.