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Multiple choice
For the harmonic oscillator with
x
=
(
a
+
a
†
)
/
2
x = (a + a^\dagger)/\sqrt{2}
x
=
(
a
+
a
†
)
/
2
(natural units), what is the ground-state expectation
⟨
0
∣
x
2
∣
0
⟩
\langle 0| x^2 |0\rangle
⟨
0∣
x
2
∣0
⟩
?
🔬 try it before you answer
1/4 = 0.25
1
1
/
2
1/\sqrt{2}
1/
2
≈ 0.707
1/2 = 0.5
Check answer