Adding Spin S1 and S2: A Puzzling Situation

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In summary, the conversation discusses the possible composite spins when adding two particles of different spin values together. The rule for determining these composite spins is straightforward, but the situation of two particles aligning antiparallel raises a question of whether it should be included as a possibility. The conversation also mentions a mistake in adding fractions and reassures that mistakes are common and nothing to worry about.
  • #1
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
 
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  • #2
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?
 
  • #3
That is a very good question. Thank you
 
  • #4
Am I banned for asking that? I understand if so
 
  • #5
We all make these obvious mistakes sometimes. Don't worry about it. ;)
 

1. What is the purpose of adding spin S1 and S2?

The purpose of adding spin S1 and S2 is to create a more complex and challenging puzzle situation for researchers to study. By introducing two different spins, the puzzle becomes more difficult to solve and requires more advanced problem-solving skills.

2. How do the spins S1 and S2 affect the puzzle?

The spins S1 and S2 add an extra layer of complexity to the puzzle. The spins determine the direction and orientation of the puzzle pieces, making it more difficult to match them up correctly. This presents a unique challenge for scientists to explore and understand.

3. What are the potential implications of this puzzle for scientific research?

This puzzle can have various implications for scientific research. It can help scientists understand the properties of spins and how they affect different systems. Additionally, it can also provide insights into complex problem-solving skills and how they develop in individuals.

4. Are there any real-world applications for this puzzle?

While the puzzle itself may not have direct real-world applications, the research surrounding it can have implications for various fields such as materials science, quantum mechanics, and cognitive psychology. Understanding spins and problem-solving skills can have practical applications in these areas.

5. How can we approach solving a puzzle with spins S1 and S2?

Solving a puzzle with spins S1 and S2 requires a strategic and analytical approach. It is essential to carefully observe the puzzle pieces and their orientations and then try to find patterns or connections between them. It also helps to have knowledge of spin properties and problem-solving techniques to effectively solve the puzzle.

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