Barrier Penetration

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Barrier Penetration and Quantum Mechanical
Tunneling
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The potential "barrier" defined
but what if we turn it upside down? This is a
finite potential barrier.
Weve learned about this situation the finite
potential well
I
II
III
U
E
-L/2
L/2
When we solved this problem, our solutions looked
like this
What would you expect based on your knowledge of
the finite box?
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A classical analogy more evidence of wavelike
behavior
Total Internal Reflection
(in actuality the light field in the optically
dense space is evanescent, i.e. exponentially
decaying)
Frustrated Total Internal Reflection
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Frustrated Total Internal Reflection dependence
on layer thickness
Below, the thick curves show the reflectance as
the thickness of the low-index layer (air)
changes from 10 to 900 nm. Note that as the layer
thickness increases, the reflectance becomes
closer to total at 41 degrees. That is, FTR gives
way to TIR.
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wave packet approaching a barrier
Qualitatively
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Pedagogical exercise consider time independent
case
(pure momentum states)
to the left of the barrier
to the right of the barrier
Instructive to consider the probability of
transmission and reflection
RT1 of course
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EgtU case
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Field emission microscope
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Real world example field emission

e
0
x
U(x)-eex
E
-U
0
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Application alpha decay
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Why does the half life vary more than the kinetic
energy?
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alpha decay
Separation of centers of alpha and nucleus at edge of barrier 9.1 fm
Height of barrier 26.4 MeV
Radius at which barrier drops to alpha energy 26.9 fm
Width of barrier seen by alpha 17.9 fm
Alpha's frequency of hitting the barrier 1.1 x 1021/s
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Real world application smoke detector
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An aside another kind of smoke detector
The photoelectric detector
Without smoke
With smoke