2. Consider operators A and B whose matrices are, 1 3 0 10-2 0 0 0...

 

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2. Consider operators A and B whose matrices are, 1 3 0 10-2 0 0 0 -1 -20 A = 1 0 1 0 (a) Are A and B Hermitian? (b) Do A and B commute? (c) Find the eigenvalues and eigenvectors of B. (d) Verify that B is diagonal, being the matrix of the normalized eigenvectors of B. (e) Verify that =. (3) (3) (8) (4) (2) [20] 2. Consider operators A and B whose matrices are, 1 3 0 10-2 0 0 0 -1 -20 A = 1 0 1 0 (a) Are A and B Hermitian? (b) Do A and B commute? (c) Find the eigenvalues and eigenvectors of B. (d) Verify that B is diagonal, being the matrix of the normalized eigenvectors of B. (e) Verify that =. (3) (3) (8) (4) (2) [20]