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Suppose I keep a single electron inside a hollow metallic/conducting shell,what will the charge distribution on the surfaces of the shell?

Now in principle from Maxwell's equations,it simply should be charge of magnitude $e$ spread over the surface which is impossible due to quantization.So in the real world,what will be the distribution?

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I think that question is subtly different: It asks about the classical dynamics problem where there is a continuum of equally low-energy ground states (the fact that these are electrons on a conductor is irrelevant), whereas here we have the problem of quantization seeming to conflict with how symmetry demands a spread-out charge. – Chris White Aug 23 '13 at 17:50
Exactly,my question is how nature comes up with a symmetric spread-out charge while still keeping quantization intact. – Sandesh Kalantre Aug 24 '13 at 12:22

The electrons in the conduction band of a metal are delocalised, that is they do not have a precise position. The charge will end up delocalised across the whole surface and the potential over the surface will be uniform.

You say "spread over the surface which is impossible due to quantization", but in fact it is quantum mechanics that allows properties like charge to be delocalised.

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This would have been a great answer on my question :… – udiboy1209 Aug 27 '13 at 18:28

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