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Expectation value of kinetic energy

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data

    Given the following hypothetic wave function for a particle confined in a region -4≤X≤6:

    ψ(x)= A(4+x) for -4≤x≤1
    A(6-x) for 1≤x≤6
    0 otherwise


    Using the normalized wave function, calculate the expectation value of the kinetic energy.

    2. Relevant equations

    I used ∫ψ*ψdx=1 to normaize the function and got that |A|^2=3/250.

    3. The attempt at a solution
    I know that T=[itex]\frac{\hat{P^2}}{2m}[/itex]=[itex]\frac{-h^2}{2m}[/itex][itex]\frac{d^2}{dx^2}[/itex]
    I tried to calculate it using <T>=∫ψ*Tψ using the expression above and got zero which is not correct.

    The solution given by the book is <T>=-[itex]\frac{h^2}{2m}[/itex][itex]\frac{3}{250}[/itex](0*1-5*2+0*1)=[itex]\frac{3h^2}{50m}[/itex]

    p.s
    h in the formulas above is [itex]\frac{h}{2pi}[/itex]

    What am I doing wrong?

    Thanks. Y.
     
  2. jcsd
  3. Dec 4, 2013 #2
    The second derivative is not zero everywhere.
     
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