For the ground state of the quantum harmonic oscillator, find the uncertainty in position and momentum. Does Heisenberg's Uncertainty principle hold? Explain. Hint: you can use these identities, for so-called "Gaussian integrals": r+∞ 88 +∞ e ax² xe xe dx - ar² dx ax² dx 0 71 a 2a Va

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For the ground state of the quantum harmonic oscillator, find the uncertainty in position
and momentum. Does Heisenberg's Uncertainty principle hold? Explain. Hint: you can
use these identities, for so-called "Gaussian integrals":
+∞ -ax²
88
•+∞
r4x
∞
e
xe
dx =
ax²
²e
2
dx
ax² dx
0
a
a Va
2a
Transcribed Image Text:For the ground state of the quantum harmonic oscillator, find the uncertainty in position and momentum. Does Heisenberg's Uncertainty principle hold? Explain. Hint: you can use these identities, for so-called "Gaussian integrals": +∞ -ax² 88 •+∞ r4x ∞ e xe dx = ax² ²e 2 dx ax² dx 0 a a Va 2a
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