Department of Physics
Prof. R. Bundschuh
The Ohio State University
Ninth Problem Set for Physics 847 (Statistical Physics II)
Winter quarter 2004
Important date:
Mar 16 9:30am11:18am final exam
Due date:
Tuesday, Mar 9
24. Twolevel bosons
8 points
An ideal BoseEinstein gas consists of noninteracting bosons of mass
m
which have an internal
degree of freedom which can be described by assuming, that the bosons are twolevel atoms.
Bosons in the ground state have energy
E
0
=
p
2
/
2
m
, while bosons in the excited state have
energy
E
1
=
p
2
/
2
m
+ Δ, where
p
is the momentum and Δ is the excitation energy. Assume
that Δ
k
B
T
.
a) Find an equation for the BoseEinstein condensation temperature
T
c
for this gas of two
level bosons. (Hint: this equation may not be so easy to actually solve since it involves
T
c
and exp(

β
Δ) = exp(

Δ
/k
B
T
c
) at the same time.)
b) Does the existence of the internal degree of freedom raise or lower the condensation
temperature?
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 Winter '04
 BUNDSCHUH
 Physics, Fundamental physics concepts, Fermi energy, Fermi, Twodimensional Fermi gas

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