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Quantum Transmission Coefficient

  1. Sep 12, 2011 #1
    Hello. I have a question, mathematical in nature.
    Considering a potential step of height V0 and width a, the amplitude coefficient is
    [tex]
    t=\frac{2k_1k_2e^{-ik_1a}}{2k_1k_2\cos{k_2a}-i(k_1^2+k_2^2)\sin(k_2a)}
    [/tex]
    Now the transmission coefficient is
    [tex]
    T=|t|^2
    [/tex]
    So I need to find the absolute value of this expression. I thought about taking the complex conjugate of the denominator and multiply both the numerator and the denominator by this factor (in order to make the denominator real). but this is very messy.
    Is there a simpler way to find the absolute value of this expression?
    Thanks
     
  2. jcsd
  3. Sep 12, 2011 #2

    Bill_K

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    Science Advisor
    Insights Author

    Much simpler. Take the complex conjugate of both the numerator and the denominator separately. If t = N/D, then |t|2 = N*N/D*D
     
  4. Sep 12, 2011 #3
    You are of course correct. Thanks for this obvious answer :-)
     
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