Contour integral and problem of Quantum mechanics (Griffiths)

[BREAD]

Homework Statement

Homework Equations

This is solution of Griffith problem 11.16

The Attempt at a Solution

This is procedure to get a 1-D integral form of Schrödinger equation.
I don't understand why that contour integral include only one pole for each contour?

 

[TSny]

I don't understand why that contour integral include only one pole for each contour?

A pole contributes only if it is inside the closed contour. (I could be misunderstanding your question.)