The diamagnetism of free electrons

A rigorous formulation is given of the quantum theory of the diamagnetism of free electrons. It is shown that Z, the partition function in classical statistics, may be calculated for arbitrary magnetic fields and temperatures without explicit knowledge of the energy levels, and complicated arguments involving boundary electrons are therefore unnecessary. It is further shown that the phenomena which arise in Fermi-Dirac statistics are determined by the singularities of Z regarded as a function of a complex variable, and, in particular, that the poles of Z give rise to the de Haas-van Alphen effect (the periodic field dependence of the susceptibility at low temperatures). The theory confirms the results obtained in earlier treatments.