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Probably more relevant to the topic at hand, an electron in an s-state
(angular momentum L = 0 h-bar) is in some sense at rest in a way in which an
electron in a p-state (angular momentum = 1 h-bar) is not. I would be glad
to amplify on this, but I don't know how ... :) except maybe to say that
zero angular momentum "must" mean no orbital motion, which would seem to be
the only motion possible for a bound electron, therefore zero angular
momentum must mean no motion ... But maybe I should stop talking now.