How to find the geometry of singlet/triplet states?

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To determine the geometry of singlet and triplet states for two electrons, one should begin by analyzing the probability density of the system. The singlet state, characterized by a total spin momentum of 0, and the triplet state, with a spin momentum of √2h-bar, require a careful examination of electron configurations. Investigating the implications of both electrons occupying the same spatial location can provide insights into their interaction and state characteristics. Understanding these quantum states involves applying principles of quantum mechanics and spin coupling. A thorough analysis of the probability density will reveal the spatial relationships and geometrical configurations of the singlet and triplet states.
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I am completely lost with this question...

for example for 2 electrons coupling that results in a singlet state with a spin momentum of 0 or a triplet state with spin momentum √2h-bar. How would you go to find the geometry of these states?
 
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I would guess start by finding the probability density. See what happens when the two electrons occupy the same location in the two different states.
 

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