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Homework Help: Location of a Particle in a Box

  1. Mar 6, 2010 #1
    SOLVED
    (Example 6.15 from Modern Physics 3e- Serway)

    1. The problem statement, all variables and given/known data
    Compute the average position <x> for the particle in a box assuming it is in the ground state


    2. Relevant equations
    [tex]
    |\Psi|^2=(2/L)\sin^2{(\pi x/L)}
    [/tex]
    [tex]
    <x> = \int^{x_0+L}_{x_0}x|\Psi|^2dx
    [/tex]

    3. The attempt at a solution
    [tex]
    <x>=x_0+L/2-\frac{L}{2\pi}\sin{\frac{2\pi x_0}{L}}
    [/tex]

    I'm pretty sure this is the answer, however, I don't understand why I get that last term, I mean, the average position should be [tex] x_0 + L/2 [/tex] right?

    If I take [tex]x_0=0[/tex] then the answer is what I was hoping for (Indeed this is the original procedure in the book), but in the more general expression with [tex] x_0 \neq 0 [/tex] I get the previous answer.
     
    Last edited: Mar 6, 2010
  2. jcsd
  3. Mar 6, 2010 #2

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    If you take the well with [itex]x_0[/itex] at the left side, then your wavefunction should also be shifted with respect to the solution for [itex]x_0=0[/itex].

    You're missing [itex]x_0[/itex]in the expression for the wavefunction.
     
  4. Mar 6, 2010 #3
    right! Thanks.
     
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