Lect17_Scattering1DII

# Lect17_Scattering1DII - Lecture 17 Scattering in One...

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Lecture 17: Scattering in One Dimension Part 2 Phy851 Fall 2009

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Transfer Matrix For the purpose of propagating a wave through multiple elements, it is more convenient to relate the amplitudes on the right-side of the boundary to those on the left-side via the ‘Transfer Matrix’: = b a M d c d c b a + = + ( ) ( ) d c k b a k = 2 1 = b a k k d c k k 1 1 2 2 1 1 1 1 = b a k k k k d c 1 1 1 2 2 1 1 1 1 = b a k k k k k d c 1 1 2 2 2 1 1 1 1 2 1 ( ) + + = 1 2 1 2 1 2 1 2 2 2 1 2 1 , k k k k k k k k k k k M Definition of transfer matrix, M: Boundary condition equations b.c. eqs in matrix form Solve for the right amplitudes in terms of the left Calculate the inverse Multiply matrices to get: We don’t use T, because the T- matrix is something else
Extracting r and t from M Consider case a =1, b = r , c = t , and d =0 : = r M t 1 0 0 22 21 12 11 = + = + r M M t r M M 22 21 M M r = 22 ] det[ M M t = 22 21 12 11 M M M M t =

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A Generalized Transfer Matrix approach to complex scattering potentials How would you go about computing r and t for a complicated structure?
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Lect17_Scattering1DII - Lecture 17 Scattering in One...

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