Quantum Mechanics integral for Dirac Delta with abs value

[rogeralms]

Homework Statement

Break integral into positive and negative, integrate, recombine and simplify and show that it reduces to a real-valued function. (See attachments)

Homework Equations

See attachments

The Attempt at a Solution

My solution is not reducing to a real-valued function. Please see attachments

 

[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 $i$.

 

[rogeralms]

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