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Math Help - Derive the expression

  1. #1
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    Derive the expression

    Derive the expression

    \frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2}

    Using

    A+B=C+D and k_{1}A- k_{1}B  =  k_{2}C- k_{2}D

    C e^{i k_{2}L}+D e^{- ik_{2}L}  =  F e^{i k_{1}L} and k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i k_{2}L}  =   k_{1}F e^{i k_{1}L}

    k_2 L=\pi/2

    I can get

    \frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}

    But can't see how to get

    \frac{k^2_1}{k^2_2}, probably easy but can't see it.

    James
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  2. #2
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    Re: Derive the expression

    Hey bobred.

    Hint: Try dividing C+D from RHS and multiplying A-B from LHS.
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  3. #3
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    Re: Derive the expression

    Hi, I've done that but still drawing a blank, I keep going round in circles. Going to have a break.
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  4. #4
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    Re: Derive the expression

    Sorry, is there another small hint?
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  5. #5
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    Re: Derive the expression

    Can you try squaring the terms and simplifying to show that the result holds? (In other words, square both sides and collect together)
    Thanks from bobred
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  6. #6
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    Re: Derive the expression

    Hi, got it, was staring me in the face, many thanks. Bob
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