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Quantum Physics: Heinsburg Uncertainty

  1. Apr 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A laser produces light of wavelength 540 nm in an ultrashort pulse. What is the minimum duration of the pulse if the minimum uncertainty in the energy of the photons is 1.0%?


    2. Relevant equations
    ΔEΔt ≥ hbar / 2


    3. The attempt at a solution
    Now I tried a couple ways here:

    1. Using Vx = hbar / 2*Pi*elemental charge*0.010%*d giving me 11.7 m/s but soon realized that seemed wrong.
    2. Since the uncertainty in energy is 1.0%, i tried substituting it in as ΔE but my end result was wrong.

    To be honest, I may be overthinking this one but Im kinda stumped as to where to go from here. I greatly appreciate your time!

    Thank you!
     
  2. jcsd
  3. Apr 8, 2012 #2
    Is Heinsburg a town in Germany?
     
  4. Apr 8, 2012 #3
    Well first you convert wavelength to energy using

    [itex]E=h\dfrac{c}{\lambda}[/itex]

    Then you know what the precise energy of the pulse is supposed to be. But the energy is known to deviate by at least 1% from this value, so you calculate this deviaton by taking 1% of what you get from the energy-wavelength relation.

    That 1% is your uncertainty in energy, [itex]\Delta E[/itex].

    What's left then is just plug in [itex]\Delta E[/itex] to Heisenberg's uncertainty and calculate [itex]\Delta t[/itex].
     
  5. Apr 8, 2012 #4
    So going through the process,

    E = (6.626*10^-34) * (3.0 x 10^8 / 5.40 x 10^-7) = 3.68 * 10^-19

    Then taking 1% of it = 3.68 x 10^-21

    Then plugging it into Δt = h / 2*Pi*3.68 x 10^-21 = 2.86 x 10^-14

    I tried this and it was marked wrong, could my units be off or am I again using the wrong formula?

    Thanks again everyone =D

    EDIT: Yeah I mispelled the title by quite a bit
     
    Last edited: Apr 9, 2012
  6. Apr 9, 2012 #5
    I am never sure about what constant should be used in Heisenberg's uncertainty. Anyways, in your relevant equations part, you use hbar/2 but in your solution h/2pi = hbar, so your missing a "1/2".

    Another thing is that the result of these calculations is Δt, uncertainty in time (duration).What you are being asked for, is the minimum duration of the pulse.

    Pulse duration could be given by [itex]\tau\pm\Delta t[/itex] and in this case you're asked for [itex]\tau-\Delta t[/itex].
     
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