By means of a quantum mechanical phase space distribution functionintroduced by von Roos, the Schroedinger equation for a non-relativisticsystem of N identical particles with scalar interactions is transformedinto a quantum mechanical generalization of the Liouville equation,thereby formulating the problem in terms of a generalized density inphase space, a quantity of primary interest in most treatments of thecorresponding classical system (or "plasma"). This transformation permitsa parallel development of the theories of classical and quantum plasmasand thus allows the quantum many-body problem to be discussed virtuallycompletely in classical terms. In particular, a kinetic theory ofquantum plasmas is obtained by deriving the quantum analogue of the BBGKYhierarchy, and applying thereto approximation techniques similar to thoseof Rostocker and Rosenbluth, and Bogoliubov. The point of departure fromsimilar previous studies based on the Wigner distribution function is thatthe proper exchange symmetry can be tractably introduced into the formalism.
Attention is first focused on the Hartree and Hartree-Fock approximations,in which case the quantum BBGKY system reduces to a simple quantumgeneralization of the Vlasov equation. This equation is used to studythe response of spatially homogeneous systems to weak external forces,and the associated problems of plasmon and spin-wave excitations. It isalso used to derive the quantum and exchange corrected equations ofinviscid hydrodynamical transport which are then applied to the problemof sound propagation in the degenerate electron gas.
The second part of the study is concerned with the theory of themany-electron atom in the Hartree and Hartree-Fock approximations.The relevant quantum Vlasov equations lead naturally to a "statistical"theory of the atom which reduces to the Thomas-Fermi-Amaldi and Thomas Fermimodels (respectively) as ħ → 0. For ħ ≠ 0, the quantum andexchange corrections to these models are simultaneously generated. Thequantum hydrodynamical theory developed earlier is used to determinethe influence of these corrections on the boundary conditions of themodel, and a theory of the compressed atom is consequently obtained.Considered in somewhat less detail are the effects of non-zero temperature,net orbital angular momentum, relativity and correlations, as well astime dependent processes.
The final part deals with the problem of the degenerate electrongas with a uniform neutralizing background. Going beyond the Hartree-Fock approximation, the pair correlation functions for particles with"parallel" and "anti-parallel" spin are obtained by neglecting three particlecorrelations. From these functions, a quantum-mechanical collisionintegral is derived which differs from that obtained by Silinand Guernsey and conjectured by Wyld and Pines in that dynamical exchangeeffects are included. Also obtained from the pair correlation functionis an expression for the "correlation energy" which reduces in the highdensity limit to the result of Gell-Mann and Brueckner. At intermediatedensities an additional term appears in the energy due to the screeningof the exchange interaction by the dielectric properties of the medium.It is evaluated in the high density limit and found to be -0.151 r_s ln r_sRyd/electron in marked disagreement with the corresponding value obtainedby DuBois.
