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

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 lambda(ezn)/2 = l(0)/n long and, accordingly, of the maximal number of n(m) of the quantized zones of the longitudinal periodic localization with the length Delta z(nh) of the drifting free electrons in the cylindrical conductors of finite size (l(0) in length and r(0) in radius) with the axial conduction current i(0)(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 i(0)(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.

Automated summary

This article presents the approximate calculation results of the maximal value of quantum number n and the maximal number of quantized zones in cylindrical conductors. It takes into account the quantum-wave nature of electric conduction current and verifies its validity in engineering fields such as high-voltage high-current pulse equipment and electromagnetic metal processing.