Understanding Spin in Composite Systems

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SUMMARY

The discussion centers on the concept of spin in composite systems, specifically regarding the spin states of an electron and a proton. The valid combinations of spins are identified as \uparrow\downarrow, \downarrow\uparrow, \uparrow\uparrow, and \downarrow\downarrow. The confusion arises from the restriction to only the first two combinations due to the magnetic quantum number (m) advancing in integer steps. This limitation suggests a focus on non-excited states, potentially excluding excited hydrogen atom configurations.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly spin.
  • Familiarity with quantum numbers, specifically magnetic quantum number (m).
  • Knowledge of composite systems in quantum physics.
  • Basic concepts of electron and proton interactions.
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  • Research the implications of spin in composite quantum systems.
  • Study the role of quantum numbers in determining particle states.
  • Explore the differences between excited and non-excited atomic states.
  • Learn about the mathematical representation of spin states in quantum mechanics.
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Students and professionals in quantum physics, physicists studying atomic interactions, and anyone interested in the principles of spin in composite systems.

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Suppose you have an electron and a proton, which both can have either spin up or down. The possible combinations are:

[itex]\uparrow\downarrow, \downarrow\uparrow, \uparrow\uparrow, \downarrow\downarrow[/itex]

But for some reason my book only allows a linear combination of the two first since they both have m=0 with the argument that m should advance in integer steps. Now this is a bit weird for me, wasn't that a rule applying for each electrons spin that we are now using on the total spin of the system - how can we just do that? It seems for me that we should either choose that the rule that the spin number advances in integer steps for each electrons spin or for the total spin - because doesn't it create problems for either if we choose both?
 
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The latter two cases are an excited hydrogen atom. Maybe your book considered only non-excited atoms, that's why it was restricted to the former two cases.
 

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