Consider a physical system whose three-dimensional statespace is spanned by the orthonormal basis formed by the threekets {Je1>, le2>, Je3>}. In the basis of these three vectors, takenin this order, the Hamiltonian H^ and the two operators B^ andD^ are defined by:7i1- i2aH= hwo | -i 3 00 2B= bo-i1+iD=0.2a1+i 1- i6.2a-3awhere 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 theground state, D was measured. What are the possible values ofAD?

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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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 50EQ

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