Problems Week 6
1. Poles of the transmission coefficient.
(i) Use the identity
W(ψ−, ψ+) = 2ika−1
to prove that a−1
has zeros at k = iκn.
(ii) Use the derivative of this identity with respect to k, i.e.
W(
d
dk
ψ−, ψ+) + W(ψ−,
d
dk
ψ+) = 2ia−1
− 2ika a−2
to show that a(k) has simple poles at k = iκn.
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