NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (4), P. 559–563
HARTREEFOCK APPROXIMATION FOR THE PROBLEM OF PARTICLE STORAGE IN DEFORMED NANOLAYER
I. F. Melikhov – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverkskiy, St. Petersburg 197101, Russia; ivan.melikhov@gmail.com
I.Yu. Popov – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverkskiy, St. Petersburg 197101, Russia; popov1955@gmail.com
The paper deals with the problem of quantum particle storage in a nanolayered structures. The system of a few electrons interacting via a δ-potential is considered. The particles are placed into a two-dimensional deformed waveguide. From a mathematical point of view, the bound state of the system means that the corresponding Hamiltonian will have eigenvalues. To treat a multi-particle problem, the Hartree-Fock approach and the finite element method are used. Three different types of the perturbation are considered: deformation of the layer boundary, a small window in a wall between two layers and a bent layer. The systems of 2–10 particles with various total spins are studied. The dependence of the minimal deformation parameter, which keeps bound state on the number of particles, is given. Comparison of the storage efficiencies in those cases is made.
Keywords: discrete spectrum, multi-particle problem, waveguide.
PACS 02.30.Tb, 73.21.Ax, 03.65.Ge