Im having trouble with my thought process for spin states of a system of two electrons Using Total Spin 'S' and Total spin mag quantum numbers 'MS' as state ket |S MS> My textbook states.... " Three Symmetric Spin states Triplet spin stats for twin identical spin -1/2 particles | Up Up> = |S MS> = |1, 1> " My thought process, two half spin particles are involved so total spin S is 1/2 + 1/2=1 and two spin ups giving MS as +1/2 + 1/2 =1 " 1/√2 ( |Up Down> + |Down Up> ) = |1,0> " I see this, again two spin particles are involved so its 1 again. However this time MS we two zeros in the bracket, ( (1/2 - 1/2) + (1/2 - 1/2) ) giving overall zero. " | Up Up> = |S MS> = |1, -1> " I understand, same reasoning as point 1. Total spin as 1 from two half spin particles, and two -1/2 for MS giving -1. " One Antisymmetric spin state Singlet spin state for two identical spin-1/2 particles 1/√2 ( |Up Down> - |Down Up> ) = |0,0> " By my reasoning for the others, this has two spin particles of 1/2 so total spin should be 1 and MS zero again..... What is wrong with my though process for how the Total spin and total mag quantum numbers are worked... How are totals calculated?