Quantum Mechanics algebra - complex analysis

1. Jan 4, 2010

sxc656

Hi,

I cannot work out how the working shown in the attached pic is well, er worked out!
Could someone explain the ins and outs of the complex analysis of taking the real or imaginary parts of some formula, for example in the context of the my case.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Jan 4, 2010

Pengwuino

Remember that $$e^{ix}= cos(x) + isin(x)$$. Taking the imaginary part means you're looking at just the sine part. When you combine into that integral form, the solution is simpler.

3. Jan 4, 2010

sxc656

Is this what you mean, i am not sure about the last two lines of working.

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4. Jan 4, 2010

vela

Staff Emeritus
You can write

$$sin pr = Im(e^{ipr})$$

Because Im(z+w) = Im(z)+Im(w) and Im(az) = aIm(z) for real a, you can pull the other exponential in as well as reverse the order of Im and the integral.

5. Jan 5, 2010

sxc656

Thanks to all