# What are some examples of infinite state quantum mechanical systems that do not involve free particles?

That is, the quanta are in bound states where there are least upper bounds and greatest lower bounds to their energy states but there are at least a countably infinite many energy levels they can assume? I'm particularly interested in examples of entangled systems with this property. Any physical examples that can be created in the laboratory?

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I find it hard to understand what you're asking. What do you mean by least upper bounds? Are looking for a system whose energy is bounded above and below? If so, the hydrogen atom is an example. –  Malabarba Aug 12 '13 at 21:58