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Expectation value of momentum times position particles in a box

  1. Dec 16, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the expectation value of <p*x> aka the momentum times the position operator, for a particle in a box.

    2. Relevant equations

    Psi(x) = root(2/l) sin (n∏x/l)
    P= -ih(bar)d/dx
    X=x

    3. The attempt at a solution
    All integrals are from 0 to L
    I'm typing this on a playbook so I won't show all my steps.
    -2ih/l ∫sin(n∏x/l)d/dx(xsin(nx/l)
    Which I got to be : sinx(sinx) + xcosx. My teacher however never gave us the integral of xcosx from 0 to l. So how can I solve this?
     
  2. jcsd
  3. Dec 16, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The integral of x*cos(x)dx is equal to the integral of x*d(sin(x)). Use integration by parts.
     
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