sigmax = ((0,1),(1,0)) sigmay = ((0,-i),(i,0)) sigmaz = ((1,0),(0,-1)) sigma = (sigmax,sigmay,sigmaz) "Spin state" s = 1/sqrt(2) (1,0) + 1/sqrt(2) (0,1) s "Expectation value" dot(conj(s),transpose(sigma),s) "Spin state" s = 1/sqrt(2) (1,0) + i/sqrt(2) (0,1) s "Expectation value" dot(conj(s),transpose(sigma),s) "General linear combination of spin up and spin down" s = c1 (1,0) + c2 (0,1) s "Use these coefficients defined by angles" c1 = expcos(theta/2) c2 = expsin(theta/2) exp(i phi) c1 c2 "Verify expectation value of spin state s equals spin polarization vector P" P = (expsin(theta) expcos(phi), expsin(theta) expsin(phi), expcos(theta)) dot(conj(s),transpose(sigma),s) == P

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