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Differentiate De Broglies Theorem

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  • 16-05-2012 5:35pm
    #1
    Smythe
    Registered Users Posts: 434 ✭✭


    Someone has written down in some notes about differentiating DeBroglies Theorem.

    They've started with Px =h/λ
    (That's P sub x)

    Then they've simply said, this differentiated is:
    ΔPx = [-h/(λ^2)]Δλ

    How have they done this? What method? What have they differentiated with respect to?

    Thank you!


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    #2
    Morbert
    Registered Users Posts: 3,457 ✭✭✭Morbert


    Smythe wrote: »
    Someone has written down in some notes about differentiating DeBroglies Theorem.

    They've started with Px =h/λ
    (That's P sub x)

    Then they've simply said, this differentiated is:
    ΔPx = [-h/(λ^2)]Δλ

    How have they done this? What method? What have they differentiated with respect to?

    Thank you!

    Consider understanding it this way:

    f(x) = h/x = h x^-1

    df/dx = -1 h x^-2 = -h/x^2

    df = -h/x^2 dx

    Now just replace f with p and x with λ


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    #3
    Smythe
    Registered Users Posts: 434 ✭✭Smythe


    Thanks very much Morbert!

    It looks so easy now!


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