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Multiple choice
An observable
A
A
A
has eigenvalues
+
1
+1
+
1
and
−
1
-1
−
1
. On a given state, measurement gives
+
1
+1
+
1
with probability
3
/
4
3/4
3/4
and
−
1
-1
−
1
with probability
1
/
4
1/4
1/4
. What is the standard deviation
Δ
A
=
⟨
A
2
⟩
−
⟨
A
⟩
2
\Delta A = \sqrt{\langle A^2\rangle - \langle A\rangle^2}
Δ
A
=
⟨
A
2
⟩
−
⟨
A
⟩
2
?
🔬 try it before you answer
3
≈
1.732
\sqrt{3} \approx 1.732
3
≈
1.732
3
/
4
=
0.75
3/4 = 0.75
3/4
=
0.75
1
/
2
=
0.5
1/2 = 0.5
1/2
=
0.5
3
/
2
≈
0.866
\sqrt{3}/2 \approx 0.866
3
/2
≈
0.866
Check answer