Total Angular Momentum of Many Particles

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To find the s=0 state for the addition of the spin of four electrons, one can utilize Wigner 9j symbols, which facilitate the addition of multiple angular momenta. For two electrons, the s=1 and s=0 states can be derived from Clebsch-Gordan coefficients. The discussion highlights the relationship between these coefficients and 3j symbols, indicating that adding three angular momenta requires 6j symbols. Understanding these mathematical tools is crucial for calculating the total spin of multiple particles. Mastery of these concepts is essential for accurately determining the total angular momentum in quantum mechanics.
andrewm
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Hi,

How does one find the s=0 state for the addition of the spin of 4 (for example) electrons?

More generally, how does one obtain the total spin of 4 electrons?

I understand that for 2 electrons one can read the s=1 and s=0 states from a table of Clebsch-Gordan coefficients.
 
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To add 4 angular momenta, you can use something called Wigner 9j symbols. (Clebsch-Gordon coefficients are related to what are called 3j symbols; adding 3 angular momenta takes 6j symbols.)
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

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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