Question: Any help with this would be really appreciated! Problem 1 Consider a three-dimensional Hilbert space. In the basis defined by three orthogonal kets I1), |2),

Any help with this would be really appreciated!

Problem 1 Consider a three-dimensional Hilbert space. In the basis defined by three orthogonal kets I1), |2), and IS), the operators A and B are represented by a1 0 0 b1 0 0 A: ( 0 a2 0 )1 B: ( 0 0 b2) 0 0 a3 0 b2 0 where all the quantities are real. 3) Do the operators A and B commute? (2 points) b) Find the eigenvalues and normalized eigenvectors of both operators. (3 points) c) Assume the system is initially in a state |2). Then the observable corresponding to the operator B is measured. What are the possible results of this measurement and the probabilities of each result? After this measurement, the observable corresponding to the operator A is measured. What are the possible results of this measurement and the probabilities of each result? (4 points) d) How are questions (a) and (c) above related? (1 point)

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