I Identical Particle States in a Unidimensional Box

[JamesHG]

I have an "unidimensional" box with two identical particles in. My question is , Does it matter in which total spin state is my total function? I mean , if it is a singlet or triplet , one is antisymmetrical and the other is symmetrical, but I only integrate the function in the spatial coordinates, so any answer?

 

[Nugatory]

I have an "unidimensional" box with two identical particles in. My question is , Does it matter in which total spin state is my total function? I mean , if it is a singlet or triplet , one is antisymmetrical and the other is symmetrical, but I only integrate the function in the spatial coordinates, so any answer?

It matters. The total wave function, which includes both position and spin, must be antisymmetric under exchange of particles. Thus, the position must be symmetric if the spin is in the singlet state and antisymmetric if the spin is in the triplet state.

 

[DrDu]

If the particles are non-interacting, you can easily write down the wave-function. Take $x_2\ge x_1$ and figure out the boundary condition for $x_2=x_1$.