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Normalization of a wave function question

  1. Jul 23, 2007 #1
    A wave function (psi) equals A(exp(ix)+exp(-ix) in the region -pi<x<pi and zero elsewhere.
    Normalize the wave function and find the probability of the particle being between x=0 and pi/8


    Equation is : the integral of psi*(x,t)psi(x,t)=1 for normalization
     
  2. jcsd
  3. Jul 23, 2007 #2
    so should I integrate the (psi*)(psi) between 0 and pi/8 or first -infinity to infinity and then plug the 0 and pi/8, and how can I integrate this?
    so the integral becomes: integrate(A(e^ix)+(e^-ix)) ??
     
  4. Jul 23, 2007 #3
    Integration need only be taken over regions where a function is non-zero.

    Also- cos(x)=(e^ix+e^-ix)/2
     
  5. Jul 24, 2007 #4

    Dick

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    And that's not psi*psi in your 'integrate', it's just psi. psi*psi will be real.
     
  6. Jul 24, 2007 #5
    ok, but I didn't understand the cos(x), could you please be more specific about that, I'm new in modern physics, thanx
     
  7. Jul 24, 2007 #6

    Dick

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    It's just an identity that might - or might not - come in handy. exp(ix)=cos(x)+isin(x). So exp(ix)+exp(-ix)=2*cos(x). Nothing to do with modern physics exactly.
     
  8. Jul 24, 2007 #7

    Kurdt

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    You can replace [itex] e^{ix}+e^{-ix} = 2 cos(x)[/itex]

    Just makes the integration easier.
     
  9. Jul 24, 2007 #8
    Thanx, very useful hint
     
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