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Quantum Mechanics integral for Dirac Delta with abs value

  1. Jan 14, 2015 #1
    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
     

    Attached Files:

  2. jcsd
  3. Jan 14, 2015 #2

    TSny

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    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##.
     
  4. Jan 19, 2015 #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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