Discontinuous electric fields

[ExplosivePete]

Griffiths introduction to electrodynamics talks about how electric potential is always continuous and electric fields are continuous except in the case of a surface charge density. This seems fair assuming you can have a continuous surface charge Density, but in the real world, these densities are made up of many finite charged particles (at least if we're thinking classically). If we think of the charged particles in terms of their quantum mechanical wave functions, could that allow for continuous distributions of charge and therefore allow for discontinuous electric fields in event of a continuous surface charge density?

I don't feel great about my wording of the question. Please ask me to clarify if needed.

Thanks,

Peter

 

[John Dalton]

See,the question's language is very unclear.
Don't think according to thermodynamics but according to atomic charge.
As per I can comprehend,every material is reactive and emits certain waveforms(according to the atomic no.)
So I can conclude that a quantum mechanical wave can't allow discontinuous electric fields as every object is possessing specific unit of charge.
I am mostly from a chemistry background so I can't discuss it according to electric potential.

 

[marcusl]

It's best not to try mixing quantum mechanics into classical E&M. Classically, surface currents can be continuous (in plane of the surface) or not (J is confined to an infinitely thin layer).