An integral representation is obtained for the Green's function for the linearized one‐dimensional Krook equation with the induced electric field of the medium included. Various asymptotic expansions in time are then obtained. When the plasma frequency is set to zero, slightly modified hydrodynamic modes appear. For nonzero plasma frequency, only plasma oscillations unaffected by the collisions are present. Finally, the initial value problem corresponding to an initial wave packet of approximate wavenumber k is considered. For times long, but not too long, plasma oscillations are present for which the frequency and wavenumber satisfy the usual Landau dispersion relation for small wavenumber. After a sufficiently long time, the solution behaves like the Green's function itself and exhibits Landau damping.

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3.
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6.
Anyone desiring further details on the numerical computations or the results should communicate directly with the author.
7.
See reference 1, where the expansions are done in detail.
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9.
A similar result is contained in
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© 1963 The American Institute of Physics.
1963
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