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
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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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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Step 1: Ground state wave function defined expectations value of x calculated
VIEWStep 2: expectation value of momentum calculated
VIEWStep 3: Expectation value of position square calculated
VIEWStep 4: expectation value of momentum square calculated
VIEWStep 5: Uncertainty in position and momentum is calculated
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