Analytical description of quantum effects at current filamentation in chalcogenide glasses

Quantum effects occurring during current filamentation in a chalcogenide glass are considered. Under the conditions considered, the current filament appears as a set of concentric tubes with different temperatures. In every tube, the electron has a specific wave function and a specific energy level. The radii of the tubes appear to be proportional to natural numbers n. The dependence of maximal temperature on the electrical field is obtained. The Schroedinger equation is reduced to the first order differential equation. The type of energy of an electron at the tube is close to exciton energy dependence. The potential energy of an electron is described with the first order polynom of temperature. The temperature distribution in the filament is shown as an interference of the electron.