PHYSICS 141A
S. G. LOUIE
SPRING 2007
Problem Set #7
Due: Friday, 03/16/07
Reading:
Finish Chapter 6 and begin Chapter 7 of ISSP
(25)
1.
ISSP, Ch. 6, Problem 9:
Static magnetoconductivity tensor.
(25)
2.
Density of states—nanometric wire
.
a) Consider a nanometric wire in the form of a rectangular parallelepiped, with two sides
L
x
"
L
y
"
1
nm
and the long axis
L
z
"
1
cm.
The single particle eigenstates of the
system may be written as
"
=
sin(n
x
#
x / L
x
)sin(n
y
y / L
y
) exp(i
2
Nz).
Show that the energy of the eigenstate with quantum numbers
n
= (n
x
, n
y
)
and
N
satisfies:
E(
n
,N)
"
n
=
(
2
$
h
N)
2
/
2
m
=
AN
2
=
1 2
mv
n
(E)
2
,
where
n
#
E(
n
,N
=
0
)
and
v
is the electron velocity along the zaxis. Here
A
=
(
2
h
)
2
/
2
m
and
N =
[(E
"
n
)/ A
]. Then given that
δ
E = 2AN
N
, show that the
density of states per unit length in the z direction
D
n
at fixed
n
, with account of the two
spin orientations and the two
±
values of
N
, is
D
n
(E)
=
4
N /
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 Spring '08
 SOUZA
 Electron, Conductivity, Solid State Physics, Fundamental physics concepts, Enrico Fermi, Field electron emission, S. G. LOUIE, nanometric wire

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