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Multiple choice
Under a harmonic perturbation, first-order theory gives the transition probability
P
=
(
V
f
i
2
/
(
4
ℏ
2
)
)
⋅
sin
2
(
Δ
t
/
2
)
/
(
Δ
/
2
)
2
P = (V_{fi}^2 / (4\hbar^2)) \cdot \sin^2(\Delta t/2) / (\Delta/2)^2
P
=
(
V
f
i
2
/
(
4
ℏ
2
))
⋅
sin
2
(
Δ
t
/2
)
/
(
Δ/2
)
2
, where
Δ
=
ω
f
i
−
ω
\Delta = \omega_{fi} - \omega
Δ
=
ω
f
i
−
ω
is the detuning. With
ℏ
=
1
\hbar = 1
ℏ
=
1
,
V
f
i
=
0.4
V_{fi} = 0.4
V
f
i
=
0.4
,
ω
f
i
=
5
\omega_{fi} = 5
ω
f
i
=
5
,
ω
=
4
\omega = 4
ω
=
4
, and
t
=
2
t = 2
t
=
2
(so
Δ
=
1
\Delta = 1
Δ
=
1
), what is
P
P
P
?
≈
0.4533
\approx 0.4533
≈
0.4533
(forgot the 1/4)
≈
0.1133
\approx 0.1133
≈
0.1133
≈
0.0283
\approx 0.0283
≈
0.0283
(used
V
f
i
2
/
4
V_{fi}^2/4
V
f
i
2
/4
without the sinc factor)
≈
0.0162
\approx 0.0162
≈
0.0162
(forgot to divide by
(
Δ
/
2
)
2
(\Delta/2)^2
(
Δ/2
)
2
)
Check answer