Why is a triplet state said to have anti-parallel spins?

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Discussion Overview

The discussion revolves around the nature of the triplet state in quantum mechanics, specifically addressing the characterization of spin states as parallel or antiparallel. Participants explore the definitions and implications of these terms in the context of spin eigenfunctions and their associated total z-projected momentum.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the three spin eigenfunctions of the triplet state and questions how the third eigenfunction, which includes both +1/2 and -1/2 spins, can represent antiparallel spins.
  • Another participant clarifies that the triplet state can have total z-projected momentum values of 1, 0, or -1, indicating that parallel spins correspond to states with momentum values of 1 or -1, while antiparallel spins correspond to a momentum value of 0.
  • A participant expresses confusion about the interpretation of the third spin eigenfunction, suggesting it should represent opposite spins but noting it is an eigenfunction of the triplet state, which is said to have parallel spins.
  • Another participant asserts that the triplet state with m_z = 0 indeed has antiparallel spins, while emphasizing that a pair of parallel spins must be classified as a triplet state, contrasting it with the singlet state that exclusively has antiparallel spins.

Areas of Agreement / Disagreement

Participants express differing views on the characterization of spins in triplet and singlet states, with some asserting that triplet states can include antiparallel spins while others maintain that they primarily represent parallel spins. The discussion remains unresolved regarding the precise definitions and implications of these terms.

Contextual Notes

Participants highlight potential misunderstandings regarding the definitions of parallel and antiparallel spins, particularly in relation to the triplet and singlet states, but do not resolve these ambiguities.

Aniket1
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The triplet state can have one of the following three spin eigenfunctions:
(+1/2,+1/2)
(-1/2,-1/2)
(1/squareroot(2))*((+1/2,-1/2)+(-1/2,+1/2))
I read that this state has electrons with parallel spins (which i assume is the z component of the spin angular momentum)
I didn't understand how the third eigenfunction represents electrons with antiparallel spins when it assigns +1/2 to one electron and -1/2 to the other.
 
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The triplet state can either have total z-projected momentum of 1,0,-1. So when the electrons have parallel spins that can be state 1 or -1. When they have anti-parallel spins that is state 0. +1/2 and -1/2 are spins that point in the opposite direction, so that is the definition of anti-parallel (for a QM spin where you only have one quantization axis).
 
If +1/2 and -1/2 are spins pointing in opposite directions, the third spin eigenfunction (which has been mentioned in the question) should represent electrons with opposite spins ( or am i making a mistake in interpretating the function?). But it is an eigenfunction of the triplet state. And triplet states have parallel spins. So where is the flaw in the argument?
Also since the total z-projected momentum can be zero for a triplet state, the spins of the electrons in this case will be in opposite directions to cancel each other.
So what do we mean by parallel and antiparallel spins in triplet and singlet states?
 
No triplet states don't just have parallel spins. The triplet state with m_z = 0 has antiparallel spins. But a pair of parallel spins must be a triplet state because it cannot be a singlet state. The singlet state has only antiparallel spins. The distinction between the singlet state | 0 0 > and the triplet state |1 0> is the sign the two states mix with.
 
Thanks..
 

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