Explicit form for representing two spin 1/2 system

[onsagerian]

explicit form for representing "two spin 1/2 system"

Hello,

Are there any explicit forms(functions) for representing a "two spin(1/2) particle system" whose states are "proton1 up / proton2 up", "proton1 up / proton2 down", "proton1 down / proton2 up", "proton1 down / proton2 down"? Can it be a special form such as a "gaussian" type function, for instance?

Thank you in advance.

 

[onsagerian]

Sorry! You don't have to worry about the original question I've posted. The situation is a proton moving from left to right in a double potential well that interacts with the other proton moving in the same way in another double potential well. So, I guess a linearly combined guassian type wavefunction may be appropriate to describe the given potential wells.