Since a particle does not have a well defined position (before measurement), it also does not have a well defined velocity. But it seems like we can define a velocity distribution.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose we observe a particle at position x=0 at time t=0. If at a later time t we observe it at x, the observed velocity is v=x/t. The probability of observing it at x at time t (and hence observing velocity v), is P(v,t) = |ψ(x,t)|[itex]^{2}[/itex].

The expected value of v, will then be <v> = ∫v |ψ(x,t)|[itex]^{2}[/itex]dx = ∫(x/t) |ψ(x,t)|[itex]^{2}[/itex]dx. Since momentum p = mv, <p> = m<v> = m ∫(x/t) |ψ(x,t)|[itex]^{2}[/itex]dx.

Is this correct? Is this consistent with the known result that <p> = m d<x>/dt ?

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# Defining velocity distribution

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