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!

2 Bosons in a box

  1. Apr 4, 2006 #1
    I'm having some difficulties with the following problem:

    Consider two (spinless)free bosons in a box of volume V with periodic boundary conditions. Let the momenta of the bosons be p and q.
    a) Write down the normalized wavefunction for p is not equal to q and p = q.

    \Psi_{pq}(r1,r2)

    I thought since they are bosons Y has to be symmetric thus:

    \Psi_{pq}(r1,r2) = \frac{1}{\sqrt{2}}(\varphi_{p}(r1)\varphi_{q}(r2)+ \varphi_{p}(r2)\varphi_{q}(r1))

    Where


    \varphi_{p}(r1)\varphi_{q}(r2) = \frac{1}{(2\pi)^3}(e^(i(p \cdot r1))(e^(i(q \cdot r2))


    and


    \varphi_{p}(r2)\varphi_{q}(r1) = \frac{1}{(2\pi)^3}(e^(i(p \cdot r2))(e^(i(q \cdot r1))


    For p=q this means:

    \Psi_{pq}(r1,r2) = \frac{1}{\sqrt{2}} \frac{1}{(2\pi)^3}(2e^(i(k \cdot (r1+r2)))

    b) Show that for p is not equal to q:

    \Psi_{pq}(r,r)|^2 > |\Psi_{pp}(r,r)|^2

    But I don't know how to do this.
     
    Last edited: Apr 4, 2006
  2. jcsd
  3. Apr 4, 2006 #2

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try to fix your latex.
     
  4. Apr 4, 2006 #3
    I tried but the weird thing is that it even gives a mistake if I try something simpel as [tex]\frac{1}{2}[/tex]
     
  5. Apr 4, 2006 #4

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    try writing it without the [tex] stuff. Then people who know latex can at least read it with a bit of difficulty.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: 2 Bosons in a box
  1. Particle in a 2-D box (Replies: 1)

Loading...