"Bloch sphere" s = (cos(theta/2), sin(theta/2) exp(i phi)) Sx = 1/2 hbar ((0,1),(1,0)) Sy = 1/2 hbar ((0,-i),(i,0)) Sz = 1/2 hbar ((1,0),(0,-1)) check(dot(conj(s),Sx,s) == 1/2 hbar sin(theta) cos(phi)) check(dot(conj(s),Sy,s) == 1/2 hbar sin(theta) sin(phi)) check(dot(conj(s),Sz,s) == 1/2 hbar cos(theta)) chi = (cos(theta/2) exp(i phi1), sin(theta/2) exp(i phi2)) s = exp(-i phi1) chi check(dot(conj(chi),Sx,chi) == dot(conj(s),Sx,s)) check(dot(conj(chi),Sy,chi) == dot(conj(s),Sy,s)) check(dot(conj(chi),Sz,chi) == dot(conj(s),Sz,s)) "ok" Run