PHYS 271: Problem Set 5
Due Mon., Mar. 30, 2009 at the start of class.
1. Imagine we have a
perfect
quantum wire attached to two metal contacts. When there is no voltage applied
across the wire, each metal has a Fermi energy of 10eV. The wire has a width
d
. We are interested in the
conductance of our wire for very small applied voltages
V
.
(a) What is the smallest value of
d
for which the conductance of the wire is nonzero?
(b) Imagine we ±nd the conductance of our wire to 100
e
2
/
h
. In this case, what are the possible values of
d
?
(c) In the limit where
d
becomes very large, the conductance of the wire will roughly scale as a power of
d
, i.e.
G
∝
d
l
. Find the exponent
l
.
2. In lecture, we calculated the total transmission probability for an electron to go through two barriers sep
arated by a distance
L
by summing the amplitude for every possible path the electron could take. For two
identical barriers, each having a transmission probability
T
, we found the result:
T
total
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 Winter '10
 AashishClark
 Energy, Quantum Physics, Fermi, 10 nm, transmission probability, total transmission probability

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