- #1

atlantic

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**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:**

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.

[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?