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Plenty of other things work too, but since I'm not very good at quantum mechanics, let's consider and actual well where the height of the well corresponds with energy (ie the very bottom of the well is zero energy), and the well-digger Elwood.
Now, if this were a classical well, there'd be a rope with a bucket on it that could be lowered to any given depth. But we're dealing with quantum mechanics, so Elwood is inside the well, not on a rope, but on a ladder. Now, as Elwood moves up and down the later he can only take one step at a time. He can't take half a step, or three-quarters of a step, he is ONLY allowed to take one step at a time (or multiple steps, as long as they're integers), no ifs ands or buts, OSHA regulations.
Now, if you give Elwood energy, he'll heat up. That is, he'll climb up the ladder. Give him enough energy and he'll go right out the top, the bond will break, the atom get knocked out the shell, Elwood will be a free particle to go wondering around until he finds another well to fall down into.
Conversely, we could cool Elwood off, in which case he'll descend the ladder. We can make Elwood do work, let's say we want five steps of energy, so we take five steps from Elwood, do work with it, and Elwood will descend five steps (ignoring entropy.)
OK so far? OK, let's say we want to cool Elwood down to absolute zero, take all the energy we can from him so he'll be completely out of energy and at the bottom of the well. So we take energy from Elwood and he descends a step at a time. He gets to the last rung of the ladder above the bottom, and much to his surprise some cheeky bastard as sawed off the last couple of inches of his ladder.
So Elwood is stuck half a step above zero energy, he can't go any lower because it's half a step. This is zero point energy. He's still got some energy, but you can't take it away. This is why at absolute zero particles still have motion. Can you do work with it? No, since you can't take it away.
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