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 Band D^ are defined by: Hħwo i 30 0 02 B = bo i -i 7 1+i 1+i 1-i 6 |v(0)) = D = where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e₁ (0)) €₂ (0)) €3(0)) 2α 0 0 0 2α 0 2a 0 -3a Suppose that the initial state |$(0)> was left to evolve until t = 0. Q: After measuring operator D at t#0 and then B, what is the probability of finding the system in ground state?
Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {|e1>, |e2>, |e3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators Band D^ are defined by: Hħwo i 30 0 02 B = bo i -i 7 1+i 1+i 1-i 6 |v(0)) = D = where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e₁ (0)) €₂ (0)) €3(0)) 2α 0 0 0 2α 0 2a 0 -3a Suppose that the initial state |$(0)> was left to evolve until t = 0. Q: After measuring operator D at t#0 and then B, what is the probability of finding the system in ground state?
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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Question
![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 and then B, what is the
probability of finding the system in ground state?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff50f4ae8-c442-4ebc-923f-a7cc5ce1c716%2Fc5087658-dd06-42d7-9af8-fbc62d9eb92d%2F1hy39i6_processed.png&w=3840&q=75)
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 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 and then B, what is the
probability of finding the system in ground state?
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