Undergrad Is the spin linked to the third quantum number ?

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The discussion revolves around the relationship between the third quantum number (m) and spin in quantum mechanics. It clarifies that there is no direct linkage between the third quantum number and spin when using standard quantum labels for bound electrons. The participants acknowledge the need for specificity regarding the quantum numbers being discussed. The inquiry also touches on whether excited particles exhibit different spin characteristics compared to non-excited ones. Overall, the conversation emphasizes the distinct roles of quantum numbers in describing electron behavior.
Dinofou
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Hi everyone,

As the title says, I was wondering if the third quantum number affects spin since they are both linked by magnetism. If not, will an excited particle have a different spin than a non-excited one ?

Thanks for your answer and sorry for the possible mistakes, I'm just a young french baguette.
 
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Dinofou said:
the third quantum number

Can you give more details, or a reference, to what particular scenario you are talking about?
 
No particular linkage, at least not if you're using the standard n,l,m,s labels for a bound electron, so that the third quantum number is m.
 
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Yes I was talking about m, should've been more specific sorry. Thx for your answer.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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