# A Commutation of α and β spins

1. Oct 18, 2016

### 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.

2. Oct 23, 2016

### Staff: Admin

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Oct 24, 2016

### Staff: Mentor

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)?

4. Nov 2, 2016

### sams

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 Ms = 0) is written as:
|S,Ms> = |1,0> = 1/21/21β2 + β1α2)

Is it the same if we write:
|S,Ms> = |1,0> = 1/21/21β2 + α2β1) ?

5. Nov 2, 2016

### Staff: Mentor

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

6. Nov 2, 2016

### sams

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

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