1. Consider the two matrices: 0 0 0 1 0 M = 0 12 0 N...

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1. Consider the two matrices: 0 0 0 "1 0 M = 0 12 0 N = n2 13 0 0 X3 0 n3 n4 (1) (a) What are the possible outcomes of a measurement of M? (b) Do the two matrices commute? Hint: you can do this by direct computation, but you don't have to. (c) Let be the eigenstate of M with eigenvalue , for j = 1, 2, 3. Write |;) as a 3-component vector. (d) Compute the uncertainty of N in the state 2). 1. Consider the two matrices: 0 0 0 "1 0 M = 0 12 0 N = n2 13 0 0 X3 0 n3 n4 (1) (a) What are the possible outcomes of a measurement of M? (b) Do the two matrices commute? Hint: you can do this by direct computation, but you don't have to. (c) Let be the eigenstate of M with eigenvalue , for j = 1, 2, 3. Write |;) as a 3-component vector. (d) Compute the uncertainty of N in the state 2).