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Question about the Heisenberg Uncertainty Principle

  1. Feb 27, 2007 #1
    1. The problem statement, all variables and given/known data

    Suppose the minimum uncertainty in the position of a particle is equal to its de Broglie wavelength. If the particle has an average speed of 4.7 105 m/s, what is the minimum uncertainty in its speed?

    2. Relevant equations

    lambda=h/p & (Py)(Y) is greater than or equal to h/4pi

    3. The attempt at a solution

    I'm not really sure where to start
     
  2. jcsd
  3. Sep 14, 2008 #2
    Let LAMDA = De Broglie Wavelength
    DELTAp = uncertainty in linear momentum
    DELTAy = uncertainty in position
    DELTAv = uncertainty in speed

    (Question gives:) DELTAy = LAMDA
    Since DELTAp*DELTAy = h/(4pi), then DELTAp*LAMDA = h/(4pi)
    Thus, LAMDA = h/(4pi*DELTAp)

    Also, LAMDA = h/p

    Combine the 2: h/(4pi*DELTAp) = h/p
    So: 4pi*DELTAp = p

    p = mv, DELTAp = m*DELTAv
    4pi*m*DELTAv = mv
    4pi*DELTAv = v

    We want DELTAv, so:
    DELTAv = v/(4pi)

    tada.
     
  4. Nov 17, 2008 #3
    oh man, delta p=m*delta v was the whole key to figuring this out that I NEVER would have thought of. Thank you so much for this detailed solution!! You are the master :)
     
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