A Greeks-function formulation for the calculation of amplitudes of the de Haas-van Alphen effect is developed. The theory can be applied to the case of metals in which magnetic breakdown takes place. The exact theory is presented and then approximated by a wave-packet approach susceptible of a simple physical interpretation; this approximation is proved to involve no error for the free-electron gas. The method is then applied to a hexagonal network corresponding to the case of magnesium for magnetic fields parallel to the hexad axis. Curves are presented for the magnetic-field dependence of the amplitude of various important periods at r=l°K; they are in agreement with preliminary experimental data. The method is also proved to give a density of states which agrees with that obtained from Pippard's model for the hexagonal network of coupled orbits.

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The problem of a positron in jellium is solved in an approach involving self-consistent perturbation of a Jastrow-type state. The merits of this approach are the following: (1) The one-electron wave functions are allowed to be nonorthogonal, (2) the formalism is indifferent with regard to utilizing the Pauli exclusion principle, and (3) numerical calculations are shorter by a factor of the order of 100 in comparison with other theories. The first two points are of special importance in view of the difficulties encountered both by the Kahana formalism and the approach of Lowy and Jackson. The screening cloud obtained in this work reproduces quite well the recent results of Rubaszek and Stachowiak, as do the partial annihilation rates. A comparison with the results of other theories and with experiment is also made.

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