Statistical Physics I (8.044) Spring 2009
Assignment 11
May 6, 2009
Not to be handed in.
Readings
The reading for Chapter IX of 8.044 is Baierlein Chapters 8 and 9.
Problem Set 11, Perhaps Better Called a Study Guide
This problem set serves as a study guide for you to build your understanding of the material
in Chapter IX of 8.044. This material will be featured on your ﬁnal exam. But, you will
not turn this problem set in. Solutions will be posted late next week.
1.
A Number of TwoState Particles
Consider a collection of
N
indistinguishable noninteracting, spinless, Bose particles.
There are only two single particle energy eigenstates:
φ
0
with energy
ε
= 0 and
φ
1
with energy
ε
= Δ.
(a) How many
N
body states are there in all? How would you list them, using the
occupation number representation? What are their energies?
(b) Evaluate the partition function
Z
(
N,T
) using the canonical ensemble. [You
must evaluate the sum.]
(c) What is the probability
p
(
n
) that
n
particles will be found in the excited state
φ
1
? Make two plots of
p
(
n
) for
N
= 4; in the ﬁrst plot, take
T
= Δ
/k
B
and in
the second plot take
T
= 1000Δ
/k
B
.
(d) Now suppose that the particles were distinguishable. How many
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 Spring '09
 KrishnaRajagopal
 Physics

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