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The two terms should vanish at infinity according to the Quantum textbook of Griffiths, but I don't see how?

I mean a complex exponential is a periodic function so how can it vanish at infinity?

If you split up the first term

exp(ikx) * exp(-ax)

Take the limit of infinity of this expression

lim exp(ikx) is not defined

limit exp(-ax) turns zero

But 0 * an undefined limit is still undefined, right?

So help me out, please.

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# Limit of a complex exponential

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