MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #3
Problem 1: Clearing Impurities
Since we are asked for an approximate a
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #1
Due in hand-in box by 12:40 PM, Wednesday, February 13
Problem 1: Doping a Semicond
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Exam #2
Problem 1 (30 points) Entropy of a Surface Film
The surface tension and heat capacity at c
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Final Exam, Solutions
Problem 1 (20 points) Binary Alloy
a) Find the number of dierent ways of cho
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions, Exam #2
Problem 1 (30 points) Entropy of a Surface Film
and CA are given in terms of T
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Exam #1
Problem 1 (30 points) Quantum Dots
y
L
0
L
x
A complicated process creates quantum dots (a
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #2
Due in hand-in box by 12:40 PM, Wednesday, February 20
Problem 1: Two Quantum Parti
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Final Exam
Problem 1 (20 points) Binary Alloy
A binary alloy (ZnCu is an example) consists of N at
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #7
Due in hand-in box by 12:40 PM, Wednesday, April 3
Problem 1: Free Expansion of a G
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #10
Due in hand-in box by 4:00 PM, Friday, May 3
Problem 1: Two Identical Particles
A
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #5
Due in hand-in box by 12:40 PM, Monday, March 11
Problem 1: Correct Boltzmann Count
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #6
Due in hand-in box by 12:40 PM, Wednesday, March 20
Problem 1: Sound Waves in a Sol
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #3
Due in hand-in box by 12:40 PM, Wednesday, February 27
Problem 1: Clearing Impuriti
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #4
Due in hand-in box by 12:40 PM, Wednesday, March 6
Problem 1: Heat Capacity at Cons
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #9
Due in hand-in box by 4;00 PM, Friday, April 19
Problem 1: The Big Bang
Early in th
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Practice Exam #2
Problem 1 (35 points) Weakly Interacting Bose Gas
At low temperatures the entropy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #2
Problem 1: Two Quantum Particles
a)
p(x1 , x2 ) = | (x1 , x2 )|2
1 x1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #4
Problem 1: Heat Capacity at Constant Pressure in a Simple Fluid
Start
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #1
Problem 1: Doping a Semiconductor
a) Mentally integrate the function p
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #8
Due in hand-in box by 12:40 PM, Wednesday, April 10
Problem 1: Dust Grains in Space
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions, Practice Exam #2
Problem 1 (35 points) Weakly Interacting Bose Gas
@P
@P
a)
dP =
dT +
d
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Problem Set #11
Due in hand-in box by 4:00 PM, Friday, May 10
Problem 1: Ripplons
(k)
k
We have se
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Practice Exam #1
Problem 1 (30 points) Collision Products
3
EB/
2
1
1
2
3
4
5
EA/
A certain collis
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #5
Problem 1: Correct Boltzmann Counting
a)
= V
N
4emE
3N
3N/2
= V N [2em
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions, Problem Set #11
Problem 1: Ripplons
a)
ky
2/Lx
points/k-volume D(k) =
2/Ly
kx
b)
(2)2
L
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #10
Problem 1: Two Identical Particles
a)
Fermions:
|1, 1, 0 >
|1, 0, 1 >
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #9
Problem 1: The Big Bang
If the expansion is adiabatic,
S = 0.
S =
@F
@
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #6
Problem 1: Sound Waves in a Solid
We need to nd (@T /@P ) Q=0 . To do
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2013
Solutions to Problem Set #8
Problem 1: Dust Grains in Space
a) H is separable: the 6 variables are