As n -> inf what can we say about the density of zeroes in the amplitude and what implication would this have on position probability?
Classical Limit of Quantum Mechanics 
Place a particle in a box
At low E (n=1), the particle acts "strange" (i.e. most likely to be found at the center)
As E 
(n→∞), ψ(x,t) oscillates faster and "peaks" grow closer
⇒ position will have constant probabilitypic.twitter.com/VRGERAbNxu
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The set of zeroes is countable so the density of probability would be constant almost everywhere (in the sense of measure theory).
End of conversation
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Adding plot of the probability might help ?
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