Consider a two-dimensional system of electrons distributed on a surface of area A at T = 0 and with a compensating unifo

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Consider a two-dimensional system of electrons distributed on a
surface of area A at T = 0 and with a compensating uniform positive
background ensuring overall neutrality.
a)Consider a point charge e a distance z above the layer of
electrons. Show that the two-dimensional Fourier
transform of the bare Coulomb potential from this charge in the
electron gas is
b)Find expressions for mean field screened potential and for
screening charge distribution in the electron
layer.