Do Alpha and Beta Spins Commute in Quantum Mechanics?

  • Context: Graduate 
  • Thread starter Thread starter sams
  • Start date Start date
  • Tags Tags
    Commutation
Click For Summary

Discussion Overview

The discussion revolves around the commutation of α and β spins in quantum mechanics, specifically in the context of a two-electron system, such as a Helium atom. Participants explore the implications of this commutation on the representation of spin states.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant asks whether α and β spins commute, specifically if αβ = βα.
  • Another participant seeks clarification on what α and β represent and whether the discussion pertains to one or two particles.
  • A participant clarifies that α and β represent the spins of an electron and that the discussion considers a system of two electrons.
  • There is a question about the equivalence of two different representations of the spin wavefunction for a triplet state.
  • Another participant asserts that the two representations of the spin wavefunction are equivalent, stating that the order is not important since these are spin states and not operators.

Areas of Agreement / Disagreement

Participants generally agree on the equivalence of the two representations of the spin wavefunction, but the initial question about the commutation of α and β spins remains unresolved.

Contextual Notes

The discussion does not clarify the implications of the commutation relation on physical observables or the mathematical treatment of the spins as operators versus states.

sams
Gold Member
Messages
84
Reaction score
2
Dear Everyone,

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

Thank you for your help.
 
sams said:
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)?
 
DrClaude said:
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 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) ?
 
sams said:
Is it the same if we write:
|S,Ms> = |1,0> = 1/21/21β2 + α2β1) ?
Yes. These are spin states, so equivalent to wave functions, and not operators. The order is of no importance.
 
  • Like
Likes   Reactions: sams
DrClaude said:
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.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 26 ·
Replies
26
Views
4K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 18 ·
Replies
18
Views
5K
  • · Replies 58 ·
2
Replies
58
Views
5K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K