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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

    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


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    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.
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