Adding Spin S1 and S2: A Puzzling Situation

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Discussion Overview

The discussion revolves around the addition of quantum spins, specifically addressing the possible composite spins when combining a particle of spin 1/2 with a particle of spin 3/2. Participants explore the implications of the addition rules presented in Griffiths' Quantum, questioning the validity of certain outcomes based on the antiparallel alignment of spins.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant states the possible composite spins for a spin 1/2 and a spin 3/2 particle as 5/2 and 3/2, but questions the absence of 1 as a possible outcome from the antiparallel alignment.
  • Another participant seeks clarification on how the composite spins are derived, specifically questioning the calculation leading to 5/2 and 3/2.
  • A later reply acknowledges the question as valid, indicating a recognition of the confusion surrounding the spin addition process.
  • One participant expresses concern about potentially being banned for asking a question, reflecting a sense of apprehension in the discussion.
  • Another participant reassures that such mistakes are common and encourages a supportive atmosphere.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the inclusion of the antiparallel arrangement as a possible outcome, and the discussion remains unresolved regarding the correct interpretation of the spin addition rules.

Contextual Notes

There are limitations in the discussion regarding the clarity of the spin addition rules and the assumptions made about antiparallel alignments, which are not fully explored or resolved.

dsr39
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I am reading the section in Griffiths' Quantum about adding spins together. It says if you have a particle of spin s1 and another of spin s2 then the possible composite spins are

s1+s2, s1+s2 -1, s1+s2-2, ... |s1-s2|

that rule (though not proven in this text) has seemed straight forward to me until now. I have a particle of spin 1/2 and a particle of spin 3/2, so I get

5/2, 3/2 ... but then the situation of them aligning antiparallel 3/2-1/2 = 1 does not occur as one of the integer steps, so do I include it as a possibility? It seems strange that the anti parallel arrangement should not be a possibility.

Thanks for the help

UPDATE:

3/2+1/2 = 2 not 2.5

One day I will figure out how to add those fractions together
 
Last edited:
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dsr39 said:
I have a particle of spin 1/2 and a particle of spin 3/2, so I get

5/2, 3/2 ...

How?
 
That is a very good question. Thank you
 
Am I banned for asking that? I understand if so
 
We all make these obvious mistakes sometimes. Don't worry about it. ;)
 

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