Some surface effects in the hydrodynamic model of metals

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Abstract
This review aims mainly to disencumber the proper heuristic functions of the model from such misconceptions, avoidable in the light of the classic papers by Block (1933), Jensen (1937) and Samoilovich (1945). The boundary conditions and linearised differential equations are established without cutoff; they determine the normal modes and orthogonality relations. The model is quantised through its normal modes, and the equal-time commutation rules are discussed. The equations in Fourier space are found; it is argued that a cutoff, if required, should be imposed on the Hamiltonian in this representation and before diagonalisation, and the consequences are explored. With such a cutoff, surface though not bulk modes become dispersive even when beta =0. The formalism is applied briefly to image potentials, and in more detail to the attraction between two half-spaces; the role of bulk modes (when beta >0) is stressed; the asymptotics are discussed at long and short distances.

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