Аннотация
A model of a quantum dot for two interacting electrons is proposed and analyzed. The properties of the ambient determining the form of the confinement potential for electrons are simulated using the electrostatic field of the image charge. Analytic expressions for the eigenvalues of each subsystem are derived taking into account the external magnetic field and using the representation of the system Hamiltonian as the sum of the Hamiltonians of the center of mass and of relative motion on the basis of the method of oscillator representation [M. Dineykhan and G. V. Efimov, Element. Chast. At. Yadra 26 , 651 (1995); M. Dineykhan, G. V. Efimov, G. Ganbold, and S. N. Nedelko, Oscillator Representation in Quantum Physics , Lecture Notes in Physics, Vol. 26, Springer, Berlin (1995)]. The relative motion of electrons is responsible for a confinement potential which differs from the parabolic confinement potential and is a function of the electron effective mass as well as the characteristics of the image charge.