The quantum molecule consisting of three quantum dots that forms a triangle with its centers is studied. The electron wave function in the nanosystem is written using the linear combination of orbital quantum wells. The dispersion equation for numerical calculations of the electron stationary states in a quantum molecule is found. A numerical calculation of the electron energy spectrum in the molecule formed by three quantum dots of a spherical shape is carried out. The influence of the nanocrystal size, the distance between them and the symmetry of the quantum molecule on the electron energy spectrum is studied. The cases of symmetry of an equilateral and an isosceles triangle are considered.

In the paper a quasi-one-dimensional three-layer nanowire (NW) with an intermediate layer at the separation boundaries is described by the Kronig-Penney model with δ-function potentials. The distance between the last or supreme atoms of the intermediate layer is a parameter of the problem and ranges from zero to two lattice parameters of crystals. A precise solution is obtained for the quantum-mechanical reflection coefficient R which makes it possible to determine the dependence of the factor on a wave vector, widths of an intermediate layer and a monolayer of the nanoheterostructure. The specific calculations are performed for the GaAs/AlAs/GaAs and AlAs/GaAs/AlAS nanowires. The comparison of the reflection coefficients in the envelope-function approximation and in the effective mass method is performed at small values of a wave vector. It is shown that similar results can be received using the refined procedure, originally proposed by Harrison, with appropriately taken parameters. For the cosinusoidal dependence of the energy on a wave vector which arises in the Kronig-Penney model within the framework of the S-matrix scattering method, we determined the binding states energy for a AlAs/GaAs/AlAs quantum well wire.