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Homework Help: Wavefunction in 1-dimension

  1. Mar 2, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the most likely position of the particle.

    2. Relevant equations

    [tex]\Psi[/tex] = A[(x+1)[tex]^{2}[/tex] - 1)]
    between x = 0 and x = 1
    [tex]\Psi[/tex] = 0 anywhere else


    3. The attempt at a solution

    I found A to equal [tex]\sqrt{15 / 38}[/tex]... but im not sure how to do the rest of it
     
  2. jcsd
  3. Mar 2, 2008 #2

    Dick

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    You didn't even have to do that if you just want the most likely position. That's at the maximum of psi*conjugate(psi), the probability density.
     
  4. Mar 3, 2008 #3
    that gives you expected value of the particles position <x>, which is the next question,
    i need to find the most likely position of the particle...
    is there another way to do this?
     
  5. Mar 3, 2008 #4

    Dick

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    No, <x> is the integral of x*psi*conjugate(psi) over the integral of psi*conjugate(psi). The 'most likely position' is the maximum of psi*conjugate(psi).
     
  6. Mar 3, 2008 #5
    so take the derivative of |psi*cojugate(psi)| and set it to 0?

    the conjugate would be A[x+1)^2 +1] ?
     
  7. Mar 3, 2008 #6

    Dick

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    Yep. And since psi is real, conjugate(psi)=psi. You'll probably notice that the maximum of psi*psi is the same as the maximum of |psi|.
     
  8. Mar 3, 2008 #7
    thanks a bunch =)
     
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