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Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, Je2>, e3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D^ are defined by: 3 i 0 7 i 1-1 0. 0. 2a H= hwo B= bo 3 0 -i 1+i 2a 0 2 1+i 1-i 6. 2a -3a where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e1| v(0) e2| »(0) (e3| v(0)) |«(0)) = 3 6. Q: Show that H and B form a CSCO.

Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, Je2>, e3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D^ are defined by: 3 i 0 7 i 1-1 0. 0. 2a H= hwo B= bo 3 0 -i 1+i 2a 0 2 1+i 1-i 6. 2a -3a where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e1| v(0) e2| »(0) (e3| v(0)) |«(0)) = 3 6. Q: Show that H and B form a CSCO.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, le2>, Je3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D^ are defined by: 7 i 1- i 2a H= hwo | -i 3 0 0 2 B= bo -i 1+i D= 0. 2a 1+i 1- i 6. 2a -3a where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: |(0) ) = (e2/ »(0) e3| v(0) Q: Show that H and B form a CSCO. Q: After measuring the energy and leaving the system in the ground state, D was measured. What are the possible values of AD?
Transcribed Image Text:Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, le2>, Je3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D^ are defined by: 7 i 1- i 2a H= hwo | -i 3 0 0 2 B= bo -i 1+i D= 0. 2a 1+i 1- i 6. 2a -3a where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: |(0) ) = (e2/ »(0) e3| v(0) Q: Show that H and B form a CSCO. Q: After measuring the energy and leaving the system in the ground state, D was measured. What are the possible values of AD?
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