Explicit form for representing two spin 1/2 system

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SUMMARY

The discussion focuses on the explicit representation of a two spin 1/2 particle system, specifically the states of two protons in various configurations: "proton1 up / proton2 up", "proton1 up / proton2 down", "proton1 down / proton2 up", and "proton1 down / proton2 down". The participants suggest that a linearly combined Gaussian-type wavefunction may be suitable for modeling the interactions of these protons in double potential wells. The inquiry emphasizes the need for specific mathematical functions to accurately depict the quantum states of the system.

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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.
 
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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.
 

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