Particle Exchange Symmetry Question

[Delber]

I am having some trouble understanding particle exchange symmetry and I'm working on the most basic problem with 2 spin-1/2 particles in a 1D infinite square well.

I understand that a singlet state requires a symmetric spatial wave function and a triplet requires an antisymmetric wave function. So my main question is can I arbitrarily just make a state that is symmetric and call that a triplet state or vice versa for a singlet state with a symmetric state? I am quite confused on the physical restrictions imposed to correctly specify the correct allowable particle states.

 

[Tangent87]

That is so weird, I literally just posted a thread on almost the exact same thing, I too find particle exchange symmetry very confusing!