Quantum Mechanics integral for Dirac Delta with abs value

  • #1
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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
 

Attachments

  • homework1.pdf
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  • HW1_1.pdf
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  • #2
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
Thank you. I see my mistake that the alpha must be kept separate. Then the result reduces to a real function.
 

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