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!

Expectation value and momentum for an infinite square well

  1. May 6, 2016 #1
    1. The problem statement, all variables and given/known data√
    A particle in an infinite square well has the initial wave function:

    [itex]Ψ(x, 0) = A x ( a - x )[/itex]

    a) Normalize Ψ(x, 0)

    b) Compute <x>, <p>, and <H> at t = 0. (Note: you cannot get <p> by differentiating <x> because you only know <x> at one instance of time)


    2. Relevant equations


    3. The attempt at a solution
    For part a, I figured out A = [itex]\sqrt{30 / a^5}[/itex]

    I'm sort of confused for part b. For <x>, I set up the integral like this:

    [itex]\int_{0}^{a}x Ψ(x, 0)^2 dx[/itex]

    And got [itex]\frac{a^6 A^2}{60}[/itex], but I'm not sure if I got it right.

    For <p> and <H>, I don't know how to set up these integrals. How would I set up these integrals? I don't need you to solve it for me, I just wanted to know how to set them up.

    Thank you for reading and helping.
     
  2. jcsd
  3. May 7, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    How does the momentum operator look like in position space, i.e. ##p_x\psi(x) =\ldots##?
     
  4. May 7, 2016 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    If you plug in your result for ##A##, you get ##\langle x \rangle = \frac a2##. Given the symmetry of ##\Psi(x,0)##, does the answer seem reasonable?
     
  5. May 7, 2016 #4
    I figured it out and got 0 for <p>. That seems reasonable right?

    Ah I didn't think of that. It makes sense.
     
  6. May 7, 2016 #5
    I also figured out <H> which turns out to be ##\frac{5 h^2}{m a^2}## which seems pretty reasonable too right?
     
  7. May 7, 2016 #6

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    Yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Expectation value and momentum for an infinite square well
Loading...