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Multiple choice
An energy eigenstate evolves as
∣
ψ
(
t
)
⟩
=
e
−
i
E
t
/
ℏ
∣
E
⟩
|\psi(t)\rangle = e^{-i E t/\hbar}|E\rangle
∣
ψ
(
t
)⟩
=
e
−
i
E
t
/ℏ
∣
E
⟩
, which here gives amplitudes
a
r
e
=
cos
(
ω
t
/
2
)
a_{re} = \cos(\omega t/2)
a
r
e
=
cos
(
ω
t
/2
)
and
a
i
m
=
sin
(
ω
t
/
2
)
a_{im} = \sin(\omega t/2)
a
im
=
sin
(
ω
t
/2
)
for a single basis component, with
ω
t
=
1.234
\omega t = 1.234
ω
t
=
1.234
. What is the total probability
a
r
e
2
+
a
i
m
2
a_{re}^2 + a_{im}^2
a
r
e
2
+
a
im
2
?
0
0.617
1
cos
(
1.234
)
\cos(1.234)
cos
(
1.234
)
≈ 0.330
Check answer