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Abstract
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In this paper, the quantum interference of plasmon excitations in the presence of charges or multipolar sources/sinks is investigated. The
effective Schr€ odinger-Poisson system for dynamical description of the arbitrary degenerate fermi gas is reduced to a set of coupled linear
pseudoforce system, and it is shown that this system admits a general multipolar solution in the 3D Cartesian coordinate. The obtained solution is then used to study well-known problems such as the double and quadruple charge interference effects. The double source interference
produces patterns quite reminiscent of that of the double slit interference with the corresponding matter-wavelength matching that of the de
Broglie wavelength of the electrons. It is found that the collective electrostatic interactions of quantum electron gas leads to the electrostatic
energy depletion around the pole which causes electrostatic polar binding in the electron fluid. The later effect which has also been previously
reported in some research seems to be an appropriate description of attractive metallic bindings. The current model is then extended to electronic interference effects in a crystal lattice with the quasiperiodic electronic states. The periodic arrangement of ionic cores in a crystal is
shown to produce different density and electrostatic potential patterns for given energy eigenvalues of the fermi gas. Moreover, a generalized
expression is obtained for electron probability current in the Schr€ odinger-Poisson model. The current model may provide a better platform
for studying the quantum interference phenomenon in complex environments such as nanocompounds and plasmonic crystals
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