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Cohen Tannoudji QM VOl.1 Chapter 1 Exercise 4 -- Eigenvalue & Fourier Transform of a Function

  1. Jan 28, 2015 #1
    1. The problem statement, all variables and given/known data
    1.jpg

    2. Relevant equations
    2.jpg

    3. The attempt at a solution

    I did Fourier transform directly to the eigenvalue equation and got

    Psi(p)=a*Psi(0)/(p^2/2m-E)

    But the rest, I don't even know where to start.
    Any opinion guys?
     
  2. jcsd
  3. Feb 1, 2015 #2
    Hi. What you got so far seems right.
    Now i can't think of any easy "trick" to show the uniqueness of E in this representation, so i would suggest you work on how to enforce:
    E(p)|φE'(p)> = δ(E–E')
    I suppose you can look up the integral; given the result you should see:
    1 - how E needs to be positive
    2 - how E must be = E' (i.e.: E is unique)
    That's a start...
     
    Last edited: Feb 1, 2015
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