# Particles in a potential box

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## Homework Statement

1000 neutral spinless particles are confined in a one-dimensional box of length 100 nm. At a given instant of time, if 100 of these particles have energy 4ε0 and the remaining 900 have energy 225ε0, then the number of particles in the left half of the box will be approximately

(a) 441

(b) 100

(c) 500

(d) 625

## The Attempt at a Solution

Energies 4ε0 and 225ε0 correspond to E2 and E15 respectively, so I tried finding the expectation value for a single particle at these energy levels which turns out to be L/2 for both. But then I thought it is irrelevant for the problem, because I can't assign a single wave function to each of the particle and carry out the calculations.

Thanks

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I think this is a misguided problem. The left side of the box is not in a particular number state, which means if you measure the number of particles of the left half of the box, the result would be probabilistic.

• phoenix95
Gold Member
I think this is a misguided problem. The left side of the box is not in a particular number state, which means if you measure the number of particles of the left half of the box, the result would be probabilistic.
In that case, how should I start? 