Longitudinal Dielectric Phenomena of the Quantum Plasma

Abstract

This didactic lecture is intended to provide an elementary introduction to some of the physical phenomena which occur in the solid state quantum plasma. In this spirit we avoid explicit discussion of the preferred tools of theoretical research in this field, namely thermodynamic Green’s functions [13, since an exposition of these elegant and powerful tools is not necessary for our present limited purpose. In fact we shall discuss many of the phenomena of the quantum plasma from a classical point of view. However, before embarking on this discussion, it is appropriate to remark briefly on an illuminating quantum mechanical formulation [2] of the problem. To start with one has the many electron Hamiltonian,

$$H = \sum\limits_i {\frac{{P_1^2}}{{2m}} + \frac{1}{2}\sum\limits_{i \ne j} {\frac{{{e^2}}}{{\left| {{{}_i} - {{}_j}} \right|}} = H_{e1}^0 + H_{e - e}^{coul.}} }$$

((1))

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