Does Displacing Electron Gas in a Slab Create a Harmonic Oscillator?

[aaaa202]

Consider a slab infinite in x,y direction but very thin in z direction. As a classical model assume that we displace the electron gas surrounding the static iron cores slightly. With this picture, does the electron gas then consitute a harmonic oscillator?
The electric field from an infinite sheet does not depend explicitly on the distance from it but somehow the charge density for this problem must do so. If we displace the electron gas more does it then see a bigger effective charge on the plane? - and why is that so

 

[Vailanor]

?No, the electron gas does not constitute a harmonic oscillator in this case. The electric field from an infinite sheet is uniform in all directions and does not depend on the distance from the sheet. Thus, displacing the electron gas will not affect the electric field and the electrons will not experience an oscillatory force. The charge density of the electron gas will be affected by the displacement of the electrons, as the electron density will be higher or lower depending on the direction of the displacement. However, this does not create an oscillatory force on the electron gas – it only affects the total charge on the plane.