1
Outline of solutions to problem set 4
Problem 5.3: a) The electric and magnetic elds are perpendicular and they are constant. Take E = E0 z and
B = B0 x and the initial velocity to be v0 y . The initial force is then,
F0 = q (E0 z + v0 B0 y x) = q (E0 v
PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #6 SOLUTIONS
(1) The Blume-Capel model is a spin-1 version of the Ising model, with Hamiltonian
H = J
ij
Si Sj
2
Si ,
i
where Si cfw_1 , 0 , +1 and where the rst sum is over all links of a lattice and the
PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #5 SOLUTIONS
(1) You know that at most one fermion may occupy any given single-particle state. A
parafermion is a particle for which the maximum occupancy of any given single-particle state
is k, where k is
PHYSICS 140B : STATISTICAL PHYSICS
HW ASSIGNMENT #1 SOLUTIONS
(1) Consider a two-dimensional gas of fermions which obey the dispersion relation
2
2
4
4
(k) = 0 (kx + ky ) a2 + 1 (kx + ky ) a4 .
2
Sketch, on the same plot, the Fermi surfaces for F = 0.1 0
PHYSICS 140A : STATISTICAL PHYSICS
HW ASSIGNMENT #6 SOLUTIONS
(1) Consider a monatomic ideal gas, represented within the grand canonical ensemble.
Show that the probability of nding the system to have N atoms is given by the Poisson
distribution,
1 N
e
N
PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #4 SOLUTIONS
(1) Consider a three-dimensional ultrarelativistic gas, with dispersion = c|k|. Find
the viral expansion of the equation of state p = p(n, T ) to order n3 for both bosons and
fermions.
Solution
PHY 203: Solutions to Problem Set 6
November 22, 2006
1
Problem 9.50
In this problem we need to calculate the differential cross section for a radial k force field of magnitude F = r3 . In order to do this, we first need to obtain the deflection angle as
PHY 203: Solutions to Problem Set 5
November 6, 2006
1 Pendulum on Sliding Block
If X is the horizontal displacement of the block the position of the pendulum
bob is given by : (X + lsinﬁ, ilcos 6). The Lagrangian for the system
is therefore
1 . 1 . . . .
a(t) =
c
t3
v(t0 ) = v0
t>1
m
c
v(t)
t = t0
t v0 c
v(t)
t0
t0
= v0 +
Z
t
dt0 v(t0 )
t0
= v0 + c
Z
t
t0
=
dt0
t03
c 1
(
2 t2
v0
1
)
t2
0
x = xf
xf v0 c
t0
t = t0
x(t)
=
Z
t
v(t0 )dt0
t0
= x0 + v0 (t
t0 )
= x0 + v0 (t
xf
t = 2t0
t0 )
= x0 + v0 (2t0
= x0 + v
1
Outline of solutions to Homework 1
Problem 1.3: For convenience we place the cube with one corner at the origin and the cube in the positive
quadrant. Then the vectors of the two body diagonals are b1 = (1, 1, 1) and b2 = (1, 1, 1). The angle between th
E xam PHYSICS 2Bb SPRING 2010 Q UIZ 4
N ame_Professor S.K. Sinha _ _ _~_ _ _ _ _ _ _ _
MULTIPLE CHOICE. C hoose t he o ne a lternative t hat b est c ompletes t he s tatement o r a nswers t he q uestion.
F igure 26.1
~-J
: 3 6.0V
40
:
~ t-Wv-fb
I
I
I
I
I
Name: Class: Date: ID: A
quiz4
Multiple Choice
Identtt the letter ofthe choice that best completes the statement or answers the question.
1. A Young's doubleslit apparatus is set up. A screen is positioned 1.60 m from the double slits and the
spacing betw
Name: Class: Date: ID: A
1c510q5
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
1. What is the wavelength of a monochromatic light beam, Where the photon energy is 3.00 eV? (h =
6.63 x 10*34 J'
PHYS 203
Princeton University
Midterm Exam Solutions
Fall 2005
1. (30 points) Bouncing Ball
A small ball of mass m is released with a zero velocity from a height h above the floor. In the
absence of air resistance the ball will hit the floor in a time t 0