A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix

representations of the spin operators are

Su

The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for

the particle is H = wS, where w = -7B. At t = 0 the wavefunction of the particle

is

ST

=

ħ 01

2

10

0

[[97]

2

i 0

1

✓10

=

ST

1

0

- [84]

ħ

2

0

-1

[3]+) +-)].

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 S₂, a constant of the motion?