Waves - bound and unbound states

quasar_4
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I was thinking about bound and unbound states the other day and want to know:

Is unboundedness a requirement for a traveling wave? That is, if you were to build a beams from bound states, would they become standing waves?
 
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Well one can decompose a traveling wave solution into an infinite sum of bound states. it's all in the time dependent coefficients.
 

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