Undergrad Hyperfine structure - Hamiltonian and bases

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The discussion centers on the computation of specific components related to hyperfine structure, with a request for clarification on the "yellow parts." It suggests that understanding the addition of angular momenta and Clebsch-Gordon coefficients may be beneficial for resolving the query. However, the initial question is deemed too vague for a comprehensive response in a forum format. Participants emphasize the need for more detail to provide effective assistance. Clearer questions are encouraged for better engagement and support.
Teri
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Hi, could you please explain me, how to copmute the yellow parts? Thank you very much.
 

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I guess, it might help to read about the addition of angular momenta and Clebsch-Gordon coefficients. Your question is too vague to be answered in a forum posting.
 
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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