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Heisenberg Uncertainty principle in 3D

  1. Feb 19, 2012 #1
    Hi there,

    So here's my assignment:

    ''The velocity of a positron is measured to be: vx=(4.00±0.18)*105 m/s, vy=(0.34±0.12)*105 m/s, vz=(1.41±0.08)*105 m/s. Within what minimum volume was the positron located at the moment the measurement was carried out?''

    I think I'm not wrong when I say that the uncertainty principle applies in every direction. Since the velocities are not relativistic, the simple equation should be:

    Δx=hbar/(2*m*Δvx)

    The same equation is used for Δy and Δz, and we only take the volume of the ''uncertainty box'' V=ΔxΔyΔz.

    With the positron having a mass of 9.109*10-31kg, that gives me V=1.12*10-25 m3. But I know the right answer is 1.4*10-26 m3.

    Even with the relativistic equations, I get the same wrong answer.

    So what am I doing wrong? Note that I never used the values of the velocities. Should I use them somewhere?

    Thank you for your time.
     
  2. jcsd
  3. Feb 20, 2012 #2
    Nevermind, there was a mistake in the book.
     
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