1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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 =)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?