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Is there a definition of a localized state in quantum mechanics? I've seen that some textbooks use this term, but they don't give a definition.

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A localized state of a particle or a field means the same thing as in semi-colloquial context: it means that most of the energy density (for the case of a field) or most of the probability (particle, quantum mechanics) may be found within a region (e.g. a ball) whose linear size is smaller (or much smaller) than the total size of the material (and surely smaller than infinity).

The opposite term is a delocalized state – e.g. a plane wave – in which the particle may be found anywhere in the material or anywhere in space.

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I suppose there's no "hard", precise definition? –  becko Sep 8 '13 at 1:36
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