Calculation of the Maximal Number of Zones of Longitudinal Periodic Localization of Drifting Electrons in the Metal Conductor with Electric Conduction Current

Abstract—The results of an approximate calculation of the maximal value of the quantum number of n = n_m for the quantized standing longitudinal electron de Broglie half-waves λ_ezn/2 = l₀/n long and, accordingly, of the maximal number of n_m of the quantized zones of the longitudinal periodic localization with the length Δz_nh of the drifting free electrons in the cylindrical conductors of finite size (l₀ in length and r₀ in radius) with the axial conduction current i₀(t) of the indicated kinds and the amplitude and time parameters (ATPs) are presented, taking into account the quantum-wave nature of the electric conduction current i₀(t) of different kinds (direct, alternating, and pulse) and ATPs in the metal conductors. The results of a verification of the calculated quantum-mechanical relationship to determine the quantum number n_m confirm its validity in such areas of engineering as high-voltage high-current pulse equipment and the electrophysical processing of metals by a strong electromagnetic field and by the pressure of a large pulse current.