# Quantum Mechanics integral for Dirac Delta with abs value

1. Jan 14, 2015

### rogeralms

1. The problem statement, all variables and given/known data
Break integral into positive and negative, integrate, recombine and simplify and show that it reduces to a real-valued function. (See attachments)

2. Relevant equations
See attachments

3. The attempt at a solution
My solution is not reducing to a real-valued function. Please see attachments

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• ###### HW1_1.pdf
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2. Jan 14, 2015

### TSny

You made the substitution $u = i k(x+\alpha-x')$. Note that expansion of this expression gives a term of the form $i k \alpha$. But in the original integral, $k \alpha$ is not multiplied by $i$.

3. Jan 19, 2015

### rogeralms

Thank you. I see my mistake that the alpha must be kept separate. Then the result reduces to a real function.