(adsbygoogle = window.adsbygoogle || []).push({}); why triplet state |1,0> is considered "parallel"?

let there be a system of two electrons and thus have s1=s2=1/2 and m1=m2=+-1/2.

the singlet state is:

|0,0> = 1/sqrt(2) ( |1/2,-1/2> - |-1/2,1/2> )

and the triplet

|1,1> = |1/2,1/2>

|1,0> = 1/sqrt(2) ( |1/2,-1/2> + |-1/2,1/2> )

|1,-1> = |-1/2,-1/2>

Since they are fermions the total wavefunction has to be antisymmetric.

So, if Stotal = 0 it has to be m1 = -m2 which leads to an antisymmetric spin function so the spacial w/f has to be symmetric.

We consider this spins' state as "antiparallel" and i can totally understand the reason.

(As i also know the spins cannot really be parallel.)

Given that the spins are antiparallel, the two electrons are permitted to occupy the same quantum state. (the rest quantum numbers,except m, to be equal).

Right?

In case Stotal = 1,

i am a bit confused.

All the three triplet states are symmetric, so the spatial w/f should then be antisymmetric.

I have read that, in this case, we consider the spins as parallel, m1 = m2

so the two electrons are not permitted to occupy the same quantum state.

For example, if they both exist in a quantum well, then the one should occupy the basic (n=1) energy state and the other should occupy the next one (n=2).

I wonder why do we consider the state:

|1,0> = 1/sqrt(2) ( |1/2,-1/2> + |-1/2,1/2> )

as "parallel" spin state and therefore enable pauli's exclusion principle ?????

Thank you for your help.

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# Why triplet state |1,0> is considered parallel ?

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