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Multiple choice
The lowering operator acts as
L
−
∣
l
,
m
⟩
=
l
(
l
+
1
)
−
m
(
m
−
1
)
∣
l
,
m
−
1
⟩
L_-|l,m\rangle = \sqrt{l(l+1) - m(m-1)}|l,m-1\rangle
L
−
∣
l
,
m
⟩
=
l
(
l
+
1
)
−
m
(
m
−
1
)
∣
l
,
m
−
1
⟩
. For
l
=
3
/
2
l = 3/2
l
=
3/2
lowering the state
m
=
+
1
/
2
m = +1/2
m
=
+
1/2
, what is the coefficient?
3
≈
1.732
\sqrt{3} \approx 1.732
3
≈
1.732
15
/
2
≈
1.936
\sqrt{15}/2 \approx 1.936
15
/2
≈
1.936
2
5
≈
2.236
\sqrt{5} \approx 2.236
5
≈
2.236
Check answer