Problem Set 9
Physics 140A
Due Tuesday March 16, 2004
1. a) Draw the band structure of a one-dimensional Fermi gas in the rst Brillouin zone. Include
h
2
all curves lying completely below E = 30( )2 2
Problem Set 8
Physics 140A
Due Tuesday March 9, 2004
Do Gersten & Smith problems 7.5 and 7.8, plus the following:
1. A thermocouple, used to measure temperatures, consists of two strips of two dierent
Answer Set 9, Physics 140A
1. a) Five portions of the free electron parabola are needed, with the last two having highest energy
h
2
E = 25 2m ( )2 at the Brillouin zone edge.
a
b) There are four dege
Answer Set 8
Physics 140A
3
1
1 k
G&S 7.5 For the density of states per unit volume, (EF ) = 22 ( 2m )3/2 EF = 22 EF =
h
2
F
1
3n
2
2 E (3 n) = 2E . Here n is the number of electrons per volume. With
Answer Set 7
Physics 140A
p2
p2
f
i
1. a) Energy conservation is Ei = Ef + h(k), or 2M = 2M + h(k), where ps represent neutron
momenta and M is the neutron mass. Using momentum conservation, we can re
Problem Set 7
Physics 140A
Due March 3, 2004
1. a) Assume that a one-dimensional crystal with lattice constant a has exactly the monatomic
chain dispersion relation. For a neutron incident on the crys
Problem Set 6
Physics 140A
Due Tuesday February 24, 2004
Do Gersten & Smith, problems 5.2, 5.4 (start by calculating the equilibrium lattice constant, then expand
the potential around that atomic spac
Answer Set 6
Physics 140A
G&S 5.2 First get the density of states. The constant- curves are circles of radius vs , and d = vs dk.
Then the area with frequency between and + d is 2 vs d . Dividing by t
Problem Set 4
Physics 140A
Due Tuesday February 10, 2004
I recommend a computer or graphing calculator for problems 2 and 5, but it isnt strictly necessary.
1. In class we looked at normal modes of a
Problem Set 5
Physics 140A
Due Tuesday February 17, 2004
This will count as a half-problem set only. Part of its purpose is to get the 130A and 140A due dates onto
dierent days.
2
1. The bulk modulus
Answer Set 5
Physics 140A
1. My denition of bulk modulus was missing a factor of V ; it should be V
2U
.
V 2
a) Since springs are 1D creatures, we rst need to relate a 3D compression to what happens t
Problem Set 2
Physics 140A
Due Thursday January 22, 2004
Do Gersten & Smith, problem 2.2, and the following:
1. We wrote the cohesive energy of a crystal by summing the interactions between all pairs
Problem Set 3
Physics 140A
Due Tuesday February 3, 2004
1. From the bi s (gi s in G&S), show that the unit cell volume in the reciprocal lattice is
where V is the unit cell volume of the real lattice.
Answer Set 2
Physics 140A
G&S 2.2: These lattice constants give info on the dierences between pairs of ionic radii. Subtracting a(NaCl) from a(KCl) gives 0.066 nm, which should be the dierence between
Answer Set 1
Physics 140A
Gersten 1.8: Consider a triangle of spheres, with a fourth sphere resting above the center of the triangle.
c
The center of the fourth sphere is 2 above the plane of the othe
Problem Set 1
Physics 140A
Due January 15, 2004
Do Gersten 1.8, plus the following:
1. Do Gersten 1.5, calculating out to tenth-nearest neighbors. On the course web page there is a C+ template
which i