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Fri. Mar. 30, 2007
Phy107 Lect 28
1
From Last Time…
Atoms:
quantized orbits
quantized energies
quantum states labeled by integers n=1,2,3…
Atomic spectra: photon emission and absorption
Fri. Mar. 30, 2007
Phy107 Lect 28
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Classical
vs
quantum
Low classical amplitude, low
energy
Higher classical amplitude,
higher energy
Fri. Mar. 30, 2007
Phy107 Lect 28
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Probability density of oscillator
Moves fast here,
low prob of finding in a
‘blind’ measurement
Moves slow here,
high prob of
finding
Classical
prob
Fri. Mar. 30, 2007
Phy107 Lect 28
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Zeropoint energy
• In all cases, wave represents the quantum
mechanical nature of the particle.
• In all cases, the lowest energy state represented
a particle with some motion.
• The particle can NEVER sit still.
• This also comes from the uncertainty principle
– If the particle were sitting still, it’s momentum would
be accurately zero.
– Means that position is completely uncertain.
Fri. Mar. 30, 2007
Phy107 Lect 28
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Unusual wave effects
•
Classically, pendulum with
particular energy never
swings beyond maximum
point.
•
This region is ‘classically
forbidden’
•
Quantum wave function
extends into classically
forbidden region.
Classically
forbidden region
End of
swing
Fri. Mar. 30, 2007
Phy107 Lect 28
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• Quantum mechanics predicts some
probability of the pendulum being found
beyond the limits of it’s swing!
• This is a common effect in quantum
mechanics, arising from wave nature of
particle.
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Fri. Mar. 30, 2007
Phy107 Lect 28
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Particle in a box, again
L
Wavefunction
Probability =
(Wavefunction)
2
Particle contained entirely
within closed tube.
Open top: particle can escape if
we shake hard enough.
But at low energies, particle
stays entirely within box.
Like an electron in metal
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 Spring '08
 n/a

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