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Free particle problem. Traveling time

  1. Mar 9, 2012 #1
    I have a particle with a known wave function, and probaility density [itex]|\Psi(x,t)|^{2}[/itex]. I also know the expectation value of the position, which is:

    [itex]<x> = x_{0} + (l\hbar/m)t[/itex],​

    where t is the time, m is the mass of the particle and [itex]x_{0}[/itex] and [itex]l[/itex] are some known constants.

    The problem is to determine how long it takes for the particle to travel a distance, y.

    I was thinking that the distance y equals the change in [itex]<x>[/itex] from the time [itex]t_{0}[/itex] to [itex]t_{1}[/itex], where ([itex]Δt = t_{1}-t_{0}[/itex]). In which case I would have to solve:

    [itex]y = x_{0} + (l\hbar/m)t_{1} - (x_{0} + (l\hbar/m)t_{0})[/itex],​

    so that the time it takes for the particle to travel the distance y is:
    [itex]Δt = (ym)/l\hbar[/itex]​

    However, I don't have the answer to this question. So would somebody tell me if me solution is correct?
  2. jcsd
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