I Solving SE for Particle in Box: Energy Level Relation

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I started learning Quantum mechanics(one dimension) a week ago and I came across solving the Schrodinger equation for a particle in a box with zero potential.I found out that there are only certain energy levels permissible for that particle. My query is if we take a large number of boxes with a particle in each, how will be the relation of number of boxes that have a given energy? Is that something governed by a law? Or does it depend on any physical condition? If so, what may it be?
 
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Hello Yayee, :welcome:

That would depend on whether there is any relationship between the boxes, I suppose. Can't think of anything physical.
 
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Okay, so if the boxes doesn't have any relationship, the relation(number of boxes having a given energy) can be arbitrary. Thank you!
 

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