1. You have a spin-1/2 quantum state described by the time-dependent wave function: |v(t)) =eidot (cos(t)...

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1. You have a spin-1/2 quantum state described by the time-dependent wave function: |v(t)) =eidot (cos(t) 1) + sin(t)| )) (a) At time t = 0, what is the probability that if you measure your spin, you will find (i) S* = (ii) Sh/2, (iii) S = -/2. (b) Calculate (S), (S), (S), as a function of time. Plot your results. (c) Calculate AST, AS as a function of time. (d) Using your results from (b) and (c), plot ASAS KS* (1) -h/2, (3) (4) Comment on the relation between the plot in (d) and the uncertainty principle. Specifically, can the graph cross below the x axis? At what times is the product ASAS as small as it is allowed to be? 1. You have a spin-1/2 quantum state described by the time-dependent wave function: |v(t)) =eidot (cos(t) 1) + sin(t)| )) (a) At time t = 0, what is the probability that if you measure your spin, you will find (i) S* = (ii) Sh/2, (iii) S = -/2. (b) Calculate (S), (S), (S), as a function of time. Plot your results. (c) Calculate AST, AS as a function of time. (d) Using your results from (b) and (c), plot ASAS KS* (1) -h/2, (3) (4) Comment on the relation between the plot in (d) and the uncertainty principle. Specifically, can the graph cross below the x axis? At what times is the product ASAS as small as it is allowed to be?