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General question about wavefunctions

  1. Apr 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Is it possible given a wavefunction ψ(x,t) to find the probability that the particle is at a particular location over an interval of time?


    2. Relevant equations



    3. The attempt at a solution
    Intuitively, given that the probability of finding the particle in a region a<x<b at a time t is ∫ab|ψ(x,t)|2dx, i would guess that the probability of finding the particle ti<t<tf at the point x would be ∫titf|ψ(x,t)|2dx. However, this leads to a bit of a paradox: this integral can leads to probabilities greater than 1, which would suggest that I am missing something pretty critical.
     
  2. jcsd
  3. Apr 29, 2012 #2
    Hi.
    If you observe the position at t=ti wave function changes or contracts so it is a mess.
    If you do not observe, you cannot say anything about position at t = ti or about staying in point x.
    Regards.
     
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