1) Spin- system is known to be in an eigenstate of S.n with eignevalue h/2, where...

 

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1) Spin- system is known to be in an eigenstate of S.n with eignevalue h/2, where n is a unit vector lying in the xz-plane that makes an angle B with the positive Z-axis. a) Suppose that S, is measured. What is the probability of getting +h/2? b) Evaluate the dispersion in S, that is ((S. - (S-))'). c) Check you answers for the special cases B = 0, 7/2, and T. 2) Using the orthogonality of |+) and |-). Prove {S;, S;} = () dij, where S, = (+)(-|+|-)(+)), Sy= (-|+)(-I+I-}(+1), S, = (1+)(+| – |-)X-1). 1) Spin- system is known to be in an eigenstate of S.n with eignevalue h/2, where n is a unit vector lying in the xz-plane that makes an angle B with the positive Z-axis. a) Suppose that S, is measured. What is the probability of getting +h/2? b) Evaluate the dispersion in S, that is ((S. - (S-))'). c) Check you answers for the special cases B = 0, 7/2, and T. 2) Using the orthogonality of |+) and |-). Prove {S;, S;} = () dij, where S, = (+)(-|+|-)(+)), Sy= (-|+)(-I+I-}(+1), S, = (1+)(+| – |-)X-1).