One-dimensional outgoing Green function

For positive

k

,

e^{ik ∣ x - x^{'} ∣}

is outgoing on both sides of

x^{'}

and obeys

(\frac{d ^{2}}{d x ^{2}} + k^{2}) e^{ik ∣ x - x^{'} ∣} = 2 ik δ (x - x^{'}) .

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