- #1
PhysicsTruth
- 117
- 18
- TL;DR Summary
- Particle in a box problem in infinite potential well with an ensemble of 100 boxes
Suppose I have 100 identical boxes of length L and the coordinates are x=0 at one end of the box and x=L at the other end, for each of them. Each has a particle of mass m. V=0 in [0,L], while it's equal to infinity in the rest of the regions. If I make a measurement on position of the particle on all the boxes at the *same time*, in how many boxes would the particle be expected to be found between x=0 and x=L/4 ?
My Approach: Probability of finding the mass m in a single box at a specific time is the integration of |psi(x)|^2 dx from x=0 to L/4. But how can we talk about the probability of 100 such identical boxes, measured at the same time? How does the probability of finding the mass m change in more than one box? How do I actually get a *number* of boxes in which the mass m can be expected to be found in [0,L/4]?
My Approach: Probability of finding the mass m in a single box at a specific time is the integration of |psi(x)|^2 dx from x=0 to L/4. But how can we talk about the probability of 100 such identical boxes, measured at the same time? How does the probability of finding the mass m change in more than one box? How do I actually get a *number* of boxes in which the mass m can be expected to be found in [0,L/4]?