do some quantum Consider a three-dimensional vector space spanned by an orthonor- mal basis |1), |2), |3). Kets |a) and |B) are given by la) = i|1) – 2|2) – i|3), IB) = i|1) + 2|3). (a) Construct (œ| and (B] (in terms of the dual basis (1|, (2|, (3|). (b) Find (a|B) and (Blæ), and confirm that (Bla) = (æ\B)*. (c) Find all nine matrix elements of the operator Ä = la)(B], in this basis, and construct the matrix A. Is it hermitian?
do some quantum Consider a three-dimensional vector space spanned by an orthonor- mal basis |1), |2), |3). Kets |a) and |B) are given by la) = i|1) – 2|2) – i|3), IB) = i|1) + 2|3). (a) Construct (œ| and (B] (in terms of the dual basis (1|, (2|, (3|). (b) Find (a|B) and (Blæ), and confirm that (Bla) = (æ\B)*. (c) Find all nine matrix elements of the operator Ä = la)(B], in this basis, and construct the matrix A. Is it hermitian?
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![Problem 5
do some quantum Consider a three-dimensional vector space spanned by an orthonor-
mal basis |1), |2), |3). Kets |a) and |B) are given by
la) = i|1) – 2|2) - i|3), IB) = i|1) + 2|3).
(a) Construct (æ| and (B| (in terms of the dual basis (1|, (2|, (3|).
(b) Find (a|B) and (Blæ), and confirm that (Bla) = (@\B)*.
(c) Find all nine matrix elements of the operator Ä = |a)(B], in this basis, and
construct the matrix A. Is it hermitian?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2F93070861-927a-4df5-b221-7ff1b1610920%2Fzlw5g8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 5
do some quantum Consider a three-dimensional vector space spanned by an orthonor-
mal basis |1), |2), |3). Kets |a) and |B) are given by
la) = i|1) – 2|2) - i|3), IB) = i|1) + 2|3).
(a) Construct (æ| and (B| (in terms of the dual basis (1|, (2|, (3|).
(b) Find (a|B) and (Blæ), and confirm that (Bla) = (@\B)*.
(c) Find all nine matrix elements of the operator Ä = |a)(B], in this basis, and
construct the matrix A. Is it hermitian?
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