Problem 30. 1989-Spring-QM-U-3.jpg ID:QM-U-653 A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix representations of the spin operators are ST = 0 [83] 1 0 = ħ 0 - ? 2 i 0 ST 1 |gbo) = √√ [3]+) + | −)]. 10 : = [1 ] The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for the particle is H=wS, where w=-B. At t= 0 the wavefunction of the particle is ħ 1 0 0 -1 1. At t = 0, S₂, is measured. What are the possible results of this measurement, and what is the probability of each being obtained? 2. Instead of measuring Sz, at t = 0, it is measured at some later time t. What are the possible results of this measurement, and what is the probability of each being, obtained? Is Sz, a constant of the motion?
Problem 30. 1989-Spring-QM-U-3.jpg ID:QM-U-653 A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix representations of the spin operators are ST = 0 [83] 1 0 = ħ 0 - ? 2 i 0 ST 1 |gbo) = √√ [3]+) + | −)]. 10 : = [1 ] The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for the particle is H=wS, where w=-B. At t= 0 the wavefunction of the particle is ħ 1 0 0 -1 1. At t = 0, S₂, is measured. What are the possible results of this measurement, and what is the probability of each being obtained? 2. Instead of measuring Sz, at t = 0, it is measured at some later time t. What are the possible results of this measurement, and what is the probability of each being, obtained? Is Sz, a constant of the motion?
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![Problem 30. 1989-Spring-QM-U-3.jpg
ID:QM-U-653
A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix
representations of the spin operators are
ŜT
=
ħ 0 1
2 1 0
7
0
$,- / [87]
Sy
2
i
0
12/0)
=
1
ŜT
: [3]+) + | −)] .
√10
=
The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for
the particle is H=wS, where w = - -B. At t = 0 the wavefunction of the particle
is
ħ
2 0
1 0
-1
]
1. At t = 0, S₂, is measured. What are the possible results of this measurement,
and what is the probability of each being obtained?
2. Instead of measuring S₂, at t = 0, it is measured at some later time t. What
are the possible results of this measurement, and what is the probability of each
being, obtained? Is Sz, a constant of the motion?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c1c0505-6119-4e49-9c75-0d7ccb62ac30%2F46d5fb4f-6755-43d8-80df-360434a47f5f%2Fn2f2uh6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 30. 1989-Spring-QM-U-3.jpg
ID:QM-U-653
A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix
representations of the spin operators are
ŜT
=
ħ 0 1
2 1 0
7
0
$,- / [87]
Sy
2
i
0
12/0)
=
1
ŜT
: [3]+) + | −)] .
√10
=
The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for
the particle is H=wS, where w = - -B. At t = 0 the wavefunction of the particle
is
ħ
2 0
1 0
-1
]
1. At t = 0, S₂, is measured. What are the possible results of this measurement,
and what is the probability of each being obtained?
2. Instead of measuring S₂, at t = 0, it is measured at some later time t. What
are the possible results of this measurement, and what is the probability of each
being, obtained? Is Sz, a constant of the motion?
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