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

  • #1

Homework Statement


1.jpg


Homework Equations


2.jpg


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?
 

Answers and Replies

  • #2
205
16
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:

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