Quantum Transmission Coefficient


by PineApple2
Tags: coefficient, quantum, transmission
PineApple2
PineApple2 is offline
#1
Sep12-11, 12:49 PM
P: 34
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
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Bill_K
Bill_K is online now
#2
Sep12-11, 02:21 PM
Sci Advisor
Thanks
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P: 3,853
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
PineApple2
PineApple2 is offline
#3
Sep12-11, 02:47 PM
P: 34
Quote Quote by Bill_K View Post
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
You are of course correct. Thanks for this obvious answer :-)


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