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Multiple choice
The raising 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
=
1
/
2
l = 1/2
l
=
1/2
and
m
=
−
1
/
2
m = -1/2
m
=
−
1/2
, what is the coefficient
l
(
l
+
1
)
−
m
(
m
+
1
)
\sqrt{l(l+1) - m(m+1)}
l
(
l
+
1
)
−
m
(
m
+
1
)
?
3
/
2
≈
0.87
\sqrt{3}/2 \approx 0.87
3
/2
≈
0.87
1
1/2
1
/
2
≈
0.71
1/\sqrt{2} \approx 0.71
1/
2
≈
0.71
Check answer