Problem 3.26 Consider a three-dimensional vector space spanned by an orthonormal basis |1), |2),|3). Kets |a) and |B) are given by la) = i| 1) – 2 |2) – i| 3), |B) = i| 1) +2|3). (a) Construct (a| and (B| (in terms of the dual basis (1), (2), (3). (b) Find (a|B) and (B|a), and confirm that (B|a) = (a|B)*. (c) Find all nine matrix elements of the operator  = |a) (B), in this basis, and construct the matrix A. Is it hermitian?
Problem 3.26 Consider a three-dimensional vector space spanned by an orthonormal basis |1), |2),|3). Kets |a) and |B) are given by la) = i| 1) – 2 |2) – i| 3), |B) = i| 1) +2|3). (a) Construct (a| and (B| (in terms of the dual basis (1), (2), (3). (b) Find (a|B) and (B|a), and confirm that (B|a) = (a|B)*. (c) Find all nine matrix elements of the operator  = |a) (B), in this basis, and construct the matrix A. Is it hermitian?
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Transcribed Image Text:Problem 3.26 Consider a three-dimensional vector space spanned by an
orthonormal basis |1), |2),|3). Kets |a) and |B) are given by
la) = i| 1) – 2 |2) – i| 3), |B) = i| 1) +2|3).
(a) Construct (a| and (B| (in terms of the dual basis (1), (2), (3).
(b) Find (a|B) and (B|a), and confirm that (B|a) = (a|B)*.
(c) Find all nine matrix elements of the operator  = |a) (B), in this basis,
and construct the matrix A. Is it hermitian?
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