# Quantum Mechanics integral for Dirac Delta with abs value

## Homework Statement

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

See attachments

## The Attempt at a Solution

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

#### Attachments

• homework1.pdf
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• HW1_1.pdf
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## Answers and Replies

TSny
Homework Helper
Gold Member
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##.

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