2. Uncertainty and uncertainty relation for a spin-1/2 system. (a) Use the matrix representation of each component S, of

[answerhappygod]

2 Uncertainty And Uncertainty Relation For A Spin 1 2 System A Use The Matrix Representation Of Each Component S Of 1 (32.87 KiB) Viewed 195 times

2. Uncertainty and uncertainty relation for a spin-1/2 system. (a) Use the matrix representation of each component S, of S given by S₁ = ₁, i = 1,2,3 to verify the commutation relations given by [Sj, Sk] = thejki St. Here Ejkt is the totally antisymmetric tensor of rank three, defined as for an even permutation of 1,2,3 -&₁ for an odd permutation of 1,2,3 otherwise (b) A spin-1/2 particle is in the state given by ly) = c[(5 + 6i)|+) + (2-3i)|->] where c is a real normalization factor. i. Find c. ii. Determine (Sx), (S²). (Sy). (S3). (S₂). (S2), ASX, AS, and AS₂. iii. Use the uncertainty relation to obtain the lower bounds of the uncertainty products AS, AS, AS AS₂, and AS, AS, and compare with the corresponding exact uncertainty products calculated using the exact uncertainties calculated in b. Ejkl