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The electron energy spectrum and wave functions in multishell spherical quantum dot, consisting of core and two spherical shells – potential wells separated by thin potential barriers, are obtained in the framework of the effective mass approximation and single band model. The investigations are performed within the matrix method for the nanostructure driven by magnetic field using the complete set of wave functions obtained without the magnetic field. The electron dipole momentum and oscillator strengths of intraband quantum transitions as functions of the magnetic field induction are numerically calculated. In order to increase the sensibility to magnetic field, the geometric parameters of the shells are chosen in such a way that the electron in the ground state is to be located in outer spherical well, but when the magnetic field induction becomes bigger, it moves into the core. It is shown that size of the middle potential well causes the smooth change of the electron location due to the effect of magnetic field, what is displayed on optical properties of nanostructure. The calculations are performed for multishell quantum dot CdSe/ZnS/CdSe/ZnS/CdSe.

The electron - impurity binding energy and photoionization cross-section of hydrogenic impurity are studied in spherical multilayered quantum dot AlxGa1-xAs/GaAs/AlyGa1-yAs driven by external electric field. The problem is solved in the framework of the effective mass approximation and rectangular potential profiles for wells and barriers, using the method of wave function expansion over a complete set of functions obtained as exact solutions of Schrodinger equation in nanostructure without impurity and electric field. The dependence of photoionization cross-section of impurity on electric field intensity is obtained taking into account the excited states of electron. It is shown that the binding energy and photoionization cross-section strongly depend on impurity location, intensity and direction of electric field. If the field is absent, the main contribution into photoionization cross-section is produced by quantum transition of electron from the ground into the first excited state, while if the electric field acts, the main role goes to the transition between ground states of electron with and without impurity. The energy of this transition decreases when electric field intensity increases.

The theory of exciton spectrum in the array of hexagon nanotubes is developed within the Bethe method and Green functions taking into account the exciton–phonon interaction. The theory is based at the effective masses model for the excitons’ electron and hole and dielectric continuum model for the interface and confined phonons. For the InAs hexagon nanotubes embedded into InP it is proven that the calculated magnitudes of energies and intensities of quantum transitions correlate to the experimental data.

The exact solutions of Schrodinger equation for the electron in Coulomb field of donor impurity are obtained within the effective masses approximation and dielectric continuum model for the spherical quantum dot CdS/SiO2 and anti-dot ZnS/CdxZn1−xS. The dependences of electron energy spectrum and its probability density on nano-system radius are studied. The numeric calculations and analysis of oscillator strength of intersubband quantum transition from ground into first excited state at the varying radius are performed. It is shown that the oscillator strength for the big quantum dot is close to the respective value for the bulk semiconductor crystal.

The energies of electron and hole Breit–Wigner resonance quasistationary states in opened complicated cylindrical quantum wire are obtained within the effective mass approximation using the S-matrix theory. Numerical calculation is performed on the example of GaAs/AlxGa1−xAs/GaAs system. The S-matrix poles are studied in complex plane of the energies. The quasiparticle lifetimes in quasistationary resonance states as functions of nanosystem geometric sizes and longitudinal quasimomentum are obtained. It is shown that quasiparticle lifetime in resonance state exponentially decreases when quasimomentum increases.