Dmytriiev O. Application of the finite gap potentials method to calculations of electron characteristics of metals

The thesis is devoted to the finite gap potentials method development and application this method to calculations of electron characteristics of metals. The Tamm spectrum of the Shredinger equation with the finite gap potential and jump boundary condition is investigated. The Tamm spectrum existence conditions are determined and explicit expressions for the Tamm states energy are derived. The singularities of the electron component of metal thermodynamic quantities which appear when the Fermi surface changes the topology are investigated in one gap potential model. Some analytical expressions are derived; all parameters which these expressions contain depend only on band edges. The finite gap potentials method is generalized to the case of crystals with hexagonal symmetry. The elliptic potential with hexagonal symmetry is constructed, the spectrum of this potential is found, the Fermi surface of beryllium in the first double zone is built, connection between constructed potential and three-particle elliptic Calogero-Moser potential is shown.