Waves - bound and unbound states

[quasar_4]

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?

 

[maverick_starstrider]

Well one can decompose a traveling wave solution into an infinite sum of bound states. it's all in the time dependent coefficients.