# Particles in a potential box

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1. Oct 29, 2015

### phoenix95

1. The problem statement, all variables and given/known data
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
2. Relevant equations

3. 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

2. Oct 29, 2015

### Xu Shuang

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.

3. Oct 29, 2015

### phoenix95

In that case, how should I start?