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 3 i 0 i 30 0 02 7 B÷bo -i i 1- i 1+ 6 | (0)) = 7 1+i 1 - i (e₁] (0)) (€₂ (0)) (€3) (0) 0 0 2α where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: = D 0 2α 2a 0 -3a Suppose that the initial state (0)> was left to evolve until t = 0. Q: After measuring operator Ô at t #0, the operator B was measured. What are the possible values of AB?

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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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
3 i 0
i 30
0 02
7
B÷bo -i
i 1- i
1+
6
| (0)) =
7
1+i 1 - i
(e₁] (0))
(€₂ (0))
(€3) (0)
0 0 2α
where wo and bo are constants. Also using this ordered basis,
the initial state of the system is given by:
=
D 0 2a
2a 0 -3a
Suppose that the initial state (0)> was left to evolve until t = 0.
Q: After measuring operator Ô at t #0, the operator B was
measured. What are the possible values of AB?
Transcribed Image Text: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 3 i 0 i 30 0 02 7 B÷bo -i i 1- i 1+ 6 | (0)) = 7 1+i 1 - i (e₁] (0)) (€₂ (0)) (€3) (0) 0 0 2α where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: = D 0 2a 2a 0 -3a Suppose that the initial state (0)> was left to evolve until t = 0. Q: After measuring operator Ô at t #0, the operator B was measured. What are the possible values of AB?
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