Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {le1>, 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: i 0 H= hwo -i 3 0 0 2 3 7 i 1- 1 2a B= bo 7 1+i 2a 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| v(0) (e2] #(0)) (e3] v(0) |»(0)) = 3 6.
Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {le1>, 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: i 0 H= hwo -i 3 0 0 2 3 7 i 1- 1 2a B= bo 7 1+i 2a 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| v(0) (e2] #(0)) (e3] v(0) |»(0)) = 3 6.
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![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:
i 0
H= hwo -i 3 0
0 2
3
7
i
1- i
0.
0.
2a
B= bo
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:
ei| v(0))
e2| v(0)
e3] v(0))
|«(0)) =
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3088407-d92b-45ff-8ac4-2f84d26f317b%2F543a3838-83d1-47ad-8018-a31fe4283abe%2Fw8z9d6v_processed.jpeg&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 {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:
i 0
H= hwo -i 3 0
0 2
3
7
i
1- i
0.
0.
2a
B= bo
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:
ei| v(0))
e2| v(0)
e3] v(0))
|«(0)) =
3
Transcribed Image Text:Suppose that the initial state |W(0)> was left to evolve until t 0.
Q1: The operator D was then measured at time + 0.
What is <D> + AD?
Q2: After Q1, the operator B was measured. What are the
possible values of AB?
Q3: After Q3, what is the probability of finding the system in
ground state?
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