Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {|e1>, |e2>, |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: H = ħwo -i 30 0 02 B = bo 7 i 1- -i 7 1+i 1+i 1-i 6 |v(0)) = where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e₁] (0)) €₂(0)) e3 (0)) D = 1-(3) 0 0 2a 0 2a 0 2a 0 -3a Q: What is the probability that the system will be found in the ground state after measuring H at t = 0?

Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {|e1>, |e2>, |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: H = ħwo -i 30 0 02 B = bo 7 i 1- -i 7 1+i 1+i 1-i 6 |v(0)) = where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e₁] (0)) €₂(0)) e3 (0)) D = 1-(3) 0 0 2a 0 2a 0 2a 0 -3a Q: What is the probability that the system will be found in the ground state after measuring H at t = 0?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 22EQ

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