# Identical spin 1/2 particles in a box.

1. Jun 2, 2012

### phyky

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. Jun 3, 2012

### vela

Staff Emeritus
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.