1. Limited time only! Sign up for a free 30min personal 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!

Finding expectation value

  1. Jan 8, 2014 #1
    1. The problem statement, all variables and given/known data
    ψ = x3 when 0≤ x ≤a and 0 otherwise
    find <x>



    2. Relevant equations
    ∫ψ*ψdx=1


    3. The attempt at a solution
    So first I multiplied x3 times A, to get Ax3, then plugging that into the equation, I get ∫A2x6dx=1
    Then I solve that for A, getting A = [tex]\sqrt{\frac{7}{a^{7}}}[/tex]
    So I plug that value back into my integral in place of A and since I'm solving for the expectation value <x>, I plug x into that equation too? This is confusing.
     
  2. jcsd
  3. Jan 8, 2014 #2

    maajdl

    User Avatar
    Gold Member

    You have succefully normalised the wavefunction: with the A value that you calculated, the (total) probability of finding the particle anywhere is 1.
    You still need now to calculate <x> = ∫ψ* x ψ dx .

    You should find something between 0 and a, and closed to a than to 0.
     
  4. Jan 8, 2014 #3
    I'm sort of confused on what to plug in for ψ and ψ* in that equation. Ax3 for both? In that case, I get (7/8)a. That seems a little high. Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted