1. Not finding help here? Sign up for a free 30min 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!

Particle in a box: possible momentum and probability

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\Psi(x,0) = \frac{1}{\sqrt{L}}, ~~~~~~ \left|x\right| < L/2[/tex]

    At the same instant, the momentum of the particle is measured, what are the possible values, and with what probability?

    2. Relevant equations



    3. The attempt at a solution
    Well, I know that [tex]\Delta{}x = L[/tex] so can I then say that since [tex]\Delta{}p \geq \frac{\hbar}{2L}[/tex] p must be greater than the same amount?

    As far as finding the probability goes, I think I need to do the Fourier transform [tex]a(k) = \int_{-L/2}^{L/2} \frac{1}{\sqrt{L}} e^{-ikx} dx = \frac{2}{k\sqrt{L}}sin(\frac{L}{2}k) [/tex]

    Now if I take the square of a(k), how do I normalize it? What are the limits of the integral? If I normalize Psi(x) before I do the fourier transform, will it be normalized after?
     
  2. jcsd
  3. Oct 5, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    been a while since i've done these, but if psi is normalised, & you perform your fourier transform with the correct constants, the momentum expression will also be normalised. (could always check on an easy function to integrate)

    the momentum probability integral will have limits from -infinity to infinity.

    The position integration is in essence the same, however you know psi is zero outside the box
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook