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: Identical spin 1/2 particles in a box.

  1. Jun 2, 2012 #1
    1. The problem statement, all variables and given/known data
    two identical particles of spin 1/2 that confined in a cubical box of side L. find the energy and wave function (non-interacting between particles)


    2. Relevant equations
    for a cubic boxby and reducing the Schrodinger equation:
    ψ(x,y,z)=√(8/L3 ) sin((nx πx)/L)sin((ny πy)/L)sin((nz πz)/L)
    E= (ħ2 π2)/(2mL2 ) (nx2+ny2+nz2 )

    3. The attempt at a solution

    E=ε12=(ħ2 π2)/(2mL2 ) [(n_x12+n_y12+n_z12 )+(n_x22+n_y22+n_z22 ) ]
    n how about the wave function? should i find it anti-symmetry wave funtion?
    ψa(r1,r2;S1,S2)=ψs(r1,r2)χa(S1,S2)
    a(r1,r2)χs(S1,S2)
    then the wave function is combination of this?
     
    Last edited: Jun 2, 2012
  2. jcsd
  3. Jun 3, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    I think you have the basic idea. You need to find the combinations that result in an antisymmetric wave function. If you meant to say that ψs(r1,r2)χa(S1,S2)=ψa(r1,r2)χs(S1,S2), however, that's obviously wrong.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...