I have a pair of non interacting, identical 1/2 spin fermions in a one dimensional infinite square well with walls at x=0 and x=L.(adsbygoogle = window.adsbygoogle || []).push({});

One particle is in ground state, the other in first excited state.

This two-particle system has total spin quantum number S=0

I have normalized energy eigenfunctions for each and am trying to explain implication of this to symmetries of spin and spatial parts of the total wave function which I think is;

ψ_{1.2}(t) =ψ_{(x1, x2, t)}Ims1, ms2>

or for time t=0

ψ_{1.2}= ψ_{(x1, x2)}Ims1, ms2>

So what exactly is the total spin quantum number please.

I can see that the spin quantum number of a spin 1/2-particle is 1/2. So could the total spin quantum number be when adding the second part of the pair?

Additionally, if this total spin quantum number becomes S=1 when they are both in the same eigenstate what does this relate to? Are both particles now either spin-up or both spin-down?

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# Total spin quantum number

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