Do Alpha and Beta Spins Commute in Quantum Mechanics?

[sams]

Dear Everyone,

A simple question. Do α and β spins commute? In other words, can we say αβ = βα ?

Thank you for your help.

 

[DrClaude]

A simple question. Do α and β spins commute? In other words, can we say αβ = βα ?

What are α and β? And are you considering one or two particles (not that it will make much of a difference, but some context would be nice)?

 

[sams]

What are α and β? And are you considering one or two particles (not that it will make much of a difference, but some context would be nice)?

Many thanks Dr. Claude for your reply.

α and β represent the spins of an electron.

We are considering here a system of two electrons (i.e. Helium atom).
The spin wavefunction of a triplet state (S=1 and M_s = 0) is written as:
|S,M_s> = |1,0> = 1/2^1/2(α₁β₂ + β₁α₂)

Is it the same if we write:
|S,M_s> = |1,0> = 1/2^1/2(α₁β₂ + α₂β₁) ?

 

[DrClaude]

Is it the same if we write:
|S,M_s> = |1,0> = 1/2^1/2(α₁β₂ + α₂β₁) ?

Yes. These are spin states, so equivalent to wave functions, and not operators. The order is of no importance.

 

[sams]

Yes. These are spin states, so equivalent to wave functions, and not operators. The order is of no importance.

Thank you once again Dr. Claude for your reply and support.