2
3.
After transmission through the barrier,
the energy is the same.
correct
4.
After transmission through the barrier,
the wavelength is smaller.
5.
After transmission through the barrier,
the wavelength is greater.
Explanation:
It is essential to recognize that the only
thing that changes as you modify the shape
of the barrier is the transmission probability,
i.e.
the number of particles that will get
through.
Therefore only the amplitude will
change as you modify the shape of the barrier;
the energy will always remain the same.
tween
a
and
b
), what would happen to the
transmission probability?
005(part4of4)10.0points
Varying which of the following will increase
the wavelength of the transmitted wave?
With everything else held fixed, if we dou
ble the height of the barrier
U
(
x
), what will
happen to the transmission probability?
1.
More information is required.
2.
It will decrease.
correct
3.
It will stay the same.
4.
It will increase.
Explanation:
Since for tunneling we assume that
E <
U
(
x
), doubling the height of the barrier will
increase the absolute value of the integrand,
and therefore will decrease the probability
of transmission.
This also makes sense in
tuitively, since a higher barrier presents a
greater obstacle (note that for an infinitely
high
barrier,
the
transmission
probability
drops to zero).
006(part1of4)10.0points
Recall the approximate formula for transmis
sion through an arbitrary barrier from the
007(part2of4)10.0points
With everything else held fixed, if we dou
ble the height of the barrier
U
(
x
), what will
happen to the transmission probability?
video:
integraldisplay
b
a
vextendsingle
vextendsingle
vextendsingle
vextendsingle
vextendsingle
radicalbig
2
m
(
E

U
(
x
))
¯
h
vextendsingle
vextendsingle
vextendsingle
vextendsingle
vextendsingle
dx
.
Keeping everything else the same, if you dou
ble the width of the barrier (the distance be