Question

Why triplet and not singlet?

Answer 1

If we consider space variables of two electrons (identical particles) to have almost the same values, then their wavefunctions are 'almost' identical if they are in the same quantum state, ie, ψa(1) ≃ ψa(2)ψa(1) ≃ ψa(2) and ψb(1) ≃ ψb(2)ψb(1) ≃ ψb(2)[the label 1 and 2 denote the spatial co-ordinates of the electron '1' and '2' i.e. (x1,y1,z1x1,y1,z1) and (x2,y2,z2x2,y2,z2), and the labels a and b for the wavefunction denote the three quantum numbers n,l,mn,l,m of two different quantum states].

In this case, the antisymmetric space eigenfunction describing the system of two electrons is

12–√[ψa(1)ψb(2)−ψa(2)ψb(1)]≃12–√[ψb(1)ψa(2)−ψb(1)ψa(2)]≃012[ψa(1)ψb(2)−ψa(2)ψb(1)]≃12[ψb(1)ψa(2)−ψb(1)ψa(2)]≃0

and the symmetric space eigenfunction is

12–√[ψa(1)ψb(2)+ψa(2)ψb(1)]≃12–√[ψb(1)ψa(2)+ψb(1)ψa(2)]≃2–√ψb(1)ψa(2).12[ψa(1)ψb(2)+ψa(2)ψb(1)]≃12[ψb(1)ψa(2)+ψb(1)ψa(2)]≃2ψb(1)ψa(2).

So, my question is why is it that we observe 2 electrons to have parallel spin(triplet) and antisymmetric space wavefunction (whose probability density is zero) (just satisfying pauli's exclusion principle here), as compared to antiparallel spins (singlet) and symmetric spatial wavefunction? I was reading up on ferromagnetism on this wiki article and also i had asked this question about a month back in chemistry stack exchange here which wasnt really well recieved.

Answer 2

hey mate

good question

answer:-

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Singlet and Triplet Excited States: Asinglet or a triplet can form when one electron is excited to a higher energy level. ... In a triplet excited stated, the electron that is promoted has the same spin orientation (parallel) to the other unpaired electron.

hope it helps....