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I'm looking for any information about quantum models of the Faraday cage effect. I don't have a good overview of solid state physics, and I'm struggling to find anything related to this in the literature.

To be more specific: I am trying to understand the Faraday cage effect from the the perspective of quantum mechanics. The classical case (from the perspective of Maxwell's equations) is clear to me. However, I have yet to find a convincing model that takes the quantum nature of a real conductor into account. Ideally such a model would be amenable to a numerical analysis, and would reproduce the classical results in some manner. My limited understanding of solid state physics stops at the free electron gas, where interactions between the particles are ignored. I have heard of the jellium mode, and it seems that may be a good starting point.

My question can also be phrased as:

What is the simplest quantum mechanical model that can capture the qualitative behaviour of the Faraday cage effect, i.e. the screening?

'Simplest' here implies that, if possible, we can ignore QED effects (unless that is somehow central to the issue), as I imagine such a treatment would be rather complicated. Qualitative comments are also welcome.

The reason I am curious about this is because it often turns out that quantum treatments of systems leads to novel, unexpected behaviour, and I'm curious whether that is the case here.

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    $\begingroup$ Solid state physics leads to band structure leads to good models for E&M interactions with solids. Really, no ‘unexpected’ stuff until you get to metamaterials, and even then it is pretty straightforward. $\endgroup$ – Jon Custer Mar 15 '18 at 19:49
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You say that you know the free electron gas model of a conductor and Maxwell's equations. That's all you need to explain the Faraday cage effect. Even most quantum mechanical models of conductors consider the electrons as quasi-classical particles with effective masses that experience various quantum-mechanically described scattering processes in the solid and thus explain pretty quantitatively the conductivity of the conductor. For the Faraday cage effect you only need the classical response of the conduction electrons to an electric field. Everything else would only make the problem unnecessarily complicated.

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