Some magnetic properties of metals. V. Magnetic behaviour of a cylindrical system of electrons for all magnetic fields

Abstract

The Wentzel-Kramers-Brillouin method is used to solve the Schrodinger equation for an electron moving in a uniform magnetic field H, the boundary of the system being a cylinder with its axis lying along the direction of the field. It is found that there are two entirely different types of wave-function possible, one type leading to the small Landau diamagnetism of large systems discussed in part I of this series, the other to the larger diamagnetism of small systems discussed in part IV. Taking into account the occupied states of both types, the steady (non-periodic) contributions to the magnetic susceptibility are derived for all fields in both the low- and high-temperature limits, and for most fields at intermediate temperatures.