1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Expectation value of a wave function

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data

    The wave function of a state is Psi(x)= N*a(x)exp(i*p0*x/h)where a(x) is a quadratically integrable real valued function Show that the expectation value of the function is p0.

    2. Relevant equations

    3. The attempt at a solution

    The only thing I'm having a problem with is how to integrate the square of the wavefunction so that I could normalize N and put the operator p=-ih(d/dx) in the integral. So I think I know what to do, just not sure how to do it.
  2. jcsd
  3. Sep 22, 2009 #2
    First off the expectation value of what? Position?

    Also what is p0, just a real-valued constant?
  4. Sep 22, 2009 #3
    It's the expectation value of the momentum I'm after. Sorry, forgot to put that in. And yes, p0 is a real-valued constant.
  5. Sep 22, 2009 #4
    All right so to normalize the wave function the wave function squared (probability) must be one. In this case you need to integrate [itex]\Psi^{*} \Psi[/itex] over all possible values (-inf to inf) and set that equal to 1, then solve for N.
  6. Sep 22, 2009 #5
    But that's the thing. I have no idea of how to do the integral.
  7. Sep 22, 2009 #6
    Well what have you tried? Start by setting up the integral and working as far as you can.
  8. Sep 22, 2009 #7
    well I get stuck when i'm supposed to integrate a(x)^2*exp(i*2*p0*x/h). How do I do that?
  9. Sep 22, 2009 #8
    [tex] 1 = \int_{- \infty}^{\infty} \Psi^{*} \Psi dx [/tex]

    Psi* is the complex conjugate of Psi. Do you know how to take a complex conjugate?

    exp(i*2*p0*x/h) makes it seem like you're trying to do:

    [tex] 1 = \int_{- \infty}^{\infty} \Psi \Psi dx [/tex]

    When you need to be doing:

    [tex] 1 = \int_{- \infty}^{\infty} \Psi^{*} \Psi dx [/tex]
  10. Sep 22, 2009 #9
    For instance the complex conjugate of [tex]f(x) = A e^{i x}[/tex] is [tex]f(x)^{*} = A e^{-i x}[/tex] where A is a real constant.
  11. Sep 22, 2009 #10
    Thanks, I think I got it right.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook