the directions obey the commutation relations:$\hbar =1$
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the probability of finding two spins in the same direction is zero, i.e. if $a\cdot b=1$ then $p(++)=p(--)=0.$
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The spin or $SU(2)$ coherent states (atomic coherent states, Bloch coherent states) form the second most known family of coherent states.[1970s by Radcliffe, Gilmore and Perelomov]: