Solving SE for Particle in Box: Energy Level Relation

[Yajee]

I started learning Quantum mechanics(one dimension) a week ago and I came across solving the Schrödinger 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?

 

[BvU]

Hello Yayee,

That would depend on whether there is any relationship between the boxes, I suppose. Can't think of anything physical.

 

[Yajee]

Okay, so if the boxes doesn't have any relationship, the relation(number of boxes having a given energy) can be arbitrary. Thank you!