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Multiple choice
The ground-state harmonic-oscillator wavefunction (in units where it equals
A
e
−
x
2
/
2
A e^{-x^2/2}
A
e
−
x
2
/2
) has
A
=
π
−
1
/
4
A = \pi^{-1/4}
A
=
π
−
1/4
. What is the probability density
∣
ψ
(
0
)
∣
2
|\psi(0)|^2
∣
ψ
(
0
)
∣
2
at
x
=
0
x=0
x
=
0
?
🔬 try it before you answer
1
/
π
≈
0.318
1/\pi \approx 0.318
1/
π
≈
0.318
π
≈
1.772
\sqrt{\pi} \approx 1.772
π
≈
1.772
π
−
1
/
4
≈
0.751
\pi^{-1/4} \approx 0.751
π
−
1/4
≈
0.751
1
/
π
≈
0.564
1/\sqrt{\pi} \approx 0.564
1/
π
≈
0.564
Check answer