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Homework Help: How can the uncertainty relation be written as such

  1. Nov 1, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that the uncertainty relation can be written as
    Δλ Δx >= λ^2 /4π

    2. Relevant equations

    3. The attempt at a solution
    Ok the uncertainty relation is ΔpΔx >= h/2π , also p = h/λ , so substituting that I have Δh/λ Δx >= h/2π , then divide both sides by h, and multiply both sides by λ^2, so I get Δλ Δx >= λ^2 /2π , which is still not the same as the one given, I don't understand how the 2π becomes 4π
  2. jcsd
  3. Nov 1, 2015 #2

    Mister T

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    The minimum uncertainty is ##\displaystyle \frac{\hbar}{2}##.
  4. Nov 1, 2015 #3


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    Staff: Mentor

    Are you sure about that?

    I don't understand what you are doing here. How can you have Δh?
  5. Nov 1, 2015 #4


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    I assume you mean Δ(h/λ) Δx, which is hΔ(1/λ) Δx
    But that isn't what you did.
    Δ(1/λ) is not the same as 1/Δλ. What does it turn into?
  6. Nov 1, 2015 #5
    Right I had a mistake in the uncertainty relation that's why I was confused. I took care of it now, thank you for the help.
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