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?
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 {|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-)
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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7884b924-5cdd-48a3-9dc8-094cb1f0ef41%2F2254a08c-c4bf-4c32-9988-6256ff9f8c62%2F5m9jvp_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
-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-)
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?
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