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Multiple choice
For
l
=
1
l = 1
l
=
1
with basis ordering
m
=
+
1
,
0
,
−
1
m = +1, 0, -1
m
=
+
1
,
0
,
−
1
, 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
⟩
. What is the matrix element
⟨
l
,
0
∣
L
+
∣
l
,
−
1
⟩
\langle l,0| L_+ |l,-1\rangle
⟨
l
,
0∣
L
+
∣
l
,
−
1
⟩
?
3
≈
1.732
\sqrt{3} \approx 1.732
3
≈
1.732
2
≈
1.414
\sqrt{2} \approx 1.414
2
≈
1.414
1
2
Check answer