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Abstract
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The one dimensional (1D) driven quantum coupled pseudoforce system governing the dynamics of collective Langmuir electron
oscillations is used in order to investigate the effects of variety of space charge distributions on plasmon excitations of a nearly free
electron gas with an arbitrary degree of degeneracy and electron fluid temperature. A generalized closed form analytic expression
for the grand wavefunction of collective excitations in the presence of an arbitrary space charge distribution is presented based on
the stationary solutions of the driven coupled pseudoforce system which has been derived from the Schrodinger-Poisson model. The €
wavefunction and electrostatic potential profiles for some special cases such as the Heaviside charge distribution, Dirac charge sheet,
impurity charge sheet in the 1D plasmonic lattice, and the Kroning-Penney Dirac charge distributions with particular applications in
plasmonics and condensed matter physics are investigated in this paper. It is remarkably found that two parallel Dirac charged sheets
completely shield all interior plasmon excitations with any given energy value from outside electrostatic fields and charge densities.
It is also found that the presence of even a weakly charged impurity layer within a perfect 1D plasmonic crystal profoundly alters the
periodic electrostatic field of the crystal lattice, and hence, the Bloch character of the wavefunction is considered in the bandgap
theory of solids. The current investigation of electron excitations in arbitrary degenerate electron gas in the presence of static charge
distributions may be used to develop analytic models for a variety of real physical situations. It also helps in further developments of
the rapidly growing fields of nanotechnology and plasmonics.
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