Do α and β Spins Commute?

In summary, the conversation discusses the commutativity of α and β spins. It is clarified that α and β represent the spins of an electron and the system being considered is a Helium atom with two electrons. The question is raised if the spin wavefunction is the same when written in a different order, and it is confirmed that the order does not matter as these are spin states, not operators.
  • #1
sams
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Dear Everyone,

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

Thank you for your help.
 
  • #3
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)?
 
  • #4
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) ?
 
  • #5
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.
 
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  • #6
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.
 

1. What is commutation of α and β spins?

Commutation of α and β spins is a quantum mechanical phenomenon where the α and β spins of particles, such as electrons, can be interchanged or switched. This is often observed in systems with spin degree of freedom, such as in nuclear magnetic resonance experiments.

2. How does commutation of α and β spins affect the properties of particles?

The commutation of α and β spins does not affect the properties of particles themselves, but rather describes the relationship between the two spin states. This phenomenon is important in understanding the behavior of particles in quantum systems.

3. Can commutation of α and β spins be observed in everyday life?

No, commutation of α and β spins is a quantum mechanical phenomenon that can only be observed in very specific conditions, such as in experiments with particles with spin degree of freedom. It is not observable in everyday life.

4. What is the significance of commutation of α and β spins in quantum mechanics?

The commutation of α and β spins is significant in quantum mechanics because it helps to describe the behavior of particles in quantum systems. It is an important aspect of understanding the fundamental principles of quantum mechanics and has implications in various fields of physics, such as in quantum computing and quantum information theory.

5. How is commutation of α and β spins related to the Pauli exclusion principle?

The commutation of α and β spins is related to the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. The commutation of α and β spins describes the behavior of fermions, such as electrons, in quantum systems and plays a role in understanding the Pauli exclusion principle.

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