Stability of electrical charges

[fluidistic]

I've just learned by chance about http://en.wikipedia.org/wiki/Earnshaw_theorem which states that point charges cannot be maintained in a stable stationary equilibrium.

But then, what does the negative electric potential energy (in this thread : https://www.physicsforums.com/showthread.php?t=334341) mean?
So the crystal wouldn't be stable, but I would need to do some work in order to separate the charges from each other. The only remaining explanation to me is that the charges must oscillate, so there would be a stable dynamic equilibrium. Am I right?

 

[jtbell]

Earnshaw's Theorem applies to classical electromagnetism. Crystals are not classical systems... you need quantum mechanics to describe them fully, in particular the bonding between atoms.

 

[fluidistic]

Earnshaw's Theorem applies to classical electromagnetism. Crystals are not classical systems... you need quantum mechanics to describe them fully, in particular the bonding between atoms.

Thanks a lot.