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Homework Help: Uncertainty Principle Problem

  1. May 31, 2012 #1
    I'm given a form of Heisenberg's uncertainty principle in the form of:

    [tex]\Delta E\Delta t\geq h[/tex]

    I need to determine a time interval which would allow a laser to cover the whole visible spectrum, from 400 to 700nm.

    Now given the relationship is on on a relative scale I used the approximation:
    [tex]\Delta E\Delta t\approx h[/tex]

    I then used the following formula:

    and differentiated like so:
    [tex]\Delta E = -\frac{hc}{\lambda ^{2}}\Delta \lambda[/tex]
    Which I then substituted back in:

    [tex](-\frac{hc}{\lambda ^{2}}\Delta \lambda)\Delta t \approx h[/tex]

    Is this correct so far?
  2. jcsd
  3. May 31, 2012 #2
    Actually, the equation is not correct (I'm assuming h to be the planck's constant). It would be:

    $$ \delta E\mbox{ }\delta t\geq\frac{\hbar}{2}=\frac{h}{4\pi} $$

    Also, I don't see what you differentiated with respect to.
  4. May 31, 2012 #3
    I see the issue. The problem set gave us the wrong h...I'll re run it and let you know the result.

    EDIT: I'm confused now. Should I be using h bar in all of the locations? This error in the problem set has mixed me up.
    Last edited: May 31, 2012
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