Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, Je2>, Je3>}. 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 i 1 - 2a H= hwo | -i 30 0 2 B= bo -i 7 1+i D= 2a 0. 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|&(0) |v(0)) = e3| v(0) 6. Suppose that the initial state |4(0)> was left to evolve until t + 0. Q: After measuring operator Ď 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 {Je1>, Je2>, Je3>}. 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 i 1 - 2a H= hwo | -i 30 0 2 B= bo -i 7 1+i D= 2a 0. 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|&(0) |v(0)) = e3| v(0) 6. Suppose that the initial state |4(0)> was left to evolve until t + 0. Q: After measuring operator Ď 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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Transcribed Image Text:Consider a physical system whose three-dimensional state
space is spanned by the orthonormal basis formed by the three
kets {Je1>, Je2>, Je3>}. 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- i
2a
H= hwo
-i 3 0
B= bo
-i
7
1 +
2a
0.
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:
(ei|#(0)
(e2l 4(0)
e3| v(0))
|v(0)) =
3
Suppose that the initial state |U(0)> was left to evolve until t + 0.
Q: After measuring operator D and then B, what is the
probability of finding the system in ground state?
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