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Homework Help: A Particle In An Infinite Box

  1. Dec 13, 2008 #1
    1. The problem statement, all variables and given/known data

    A particle in an infinite box is in the first excited state (n=2).
    Obtain the expectation value (1/2)*<x*p+p*x>

    2. Relevant equations

    3. The attempt at a solution
    I'm completely baffled by this problem.
    Can anyone just please point me in the right direction and then ill respond with what i get (because i know im gonna get stuck again)

  2. jcsd
  3. Dec 14, 2008 #2
    Hey shlomo. As a hint, the general formula for an expectation value is is given by:

    [tex]<Q(x,p)> = \int_{-\infty}^{+\infty} \psi^* Q(x,p) \psi dx[/tex]

    where x, p are the position and momentum (quantum mechanical) operators.

    This should hopefully give you a push in the right direction. As a first suggestion, you will have to find the wave equation [tex]\psi[/tex] for your specific situation.
  4. Dec 14, 2008 #3
    ok, im gonna work on that,
    are there any websites you can recommend to help me learn this stuff?
    my Prof doesn't explain anything well...
  5. Dec 14, 2008 #4
    Well I suppose it's dependent on the situation you're in. What's the outline of the course?

    Personally, I find it to be overwhelming if given a resource that goes into far more detail than the course requires.
  6. Dec 15, 2008 #5
    i beleive the wave equation is:
    \psi(x) = Asin(kx) + Bcos(kx)
    and k=sqrt((2mE)/(h-bar)^2)

    so then the normalized wave function would be:
    \psi n(x)=sqrt(2/L)*sin((n*pi*x)/L)

    and the problem said that n=2.

    And thats where I get stuck. Am i doing it right thus far? and how do i go further?
  7. Dec 15, 2008 #6
    As far as I know so far you did right. My suggestion for the further is that you can calculate <xp> and <px> seperately ans sum them up. To do so, apply the operators with their usual orders and take their integral. I know, it seems a bit tidious but this is the only way that I think.
  8. Dec 15, 2008 #7
    ok, sounds good, can u set up on of the integrals so i can see how to do it?
    then ill try to evaluate both integrals and ill post what i get.

  9. Dec 15, 2008 #8
    For the p*x take the derivative of the x*wave function's conjugate and multiply it with the wave function itself and take the integral.
  10. Dec 15, 2008 #9
    Have you figured it out yet? I don't understand 'soul's last comment/step. I understand up to normalizing the wave function. I don't know how to derive px and xp.

  11. Dec 15, 2008 #10
    We need it for tomorrow.
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