Consider a quantum system with an observable A that has three possible measurement results: a 1 ,…

Consider a quantum system with an observable A that has three possible measurement results: a1, a2, and a3.

a) Write down the three kets  |a1), |a2), and |a3) corresponding to these possible results using matrix notation.

b) The system is prepared in the state

4afb95c0 b700 4b79 8e0a 03ecbc1bc361

Write this state in matrix notation and calculate the probabilities of all possible measurement results of the observable A. Plot a histogram of the predicted measurement results.

c) In a different experiment, the system is prepared in the state

8c6b31e7 a36f 44c6 ad56 eb58b8d715f5

Write this state in matrix notation and calculate the probabilities of all possible measurement results of the observable A. Plot a histogram of the predicted measurement results.

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