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1. A system consist of two particles,each of which has two possible quantum stats
with energies Eo and 2Eo .Write the complete expression for the partition function
(a) The particle are distinguishable.
(b) The particle obey Maxwell-Boltzmann statistics.
(c) The particle obey Fermi-Dirac statistics.
(d) The particle obey Bose-Einstein statistics.
2.When a closed cubic box of volume V is heated to temperature T, the walls will emit
and absorb electromagnetic radiation . When the radiation is in equilibrium with the
walls, an equal amount of radiation is emitted and absorbed by the walls, and the
radiation forms standing waves in the box. A standing wave of frequency  and
wave vector k is composed of photons of energy  and momentum p= k .Photons
are massless bosons.Since photons are continuously emitted and absorbed by the
walls , the number of photons in the box continuously change. Since photons are
massless , the chemical potential is zero.
(a)Find the average number of photons with momentum p.
(b)find the heat capacity of the photon gas.
3.A one-dinmensional Debye solid with N lattice sites coupled harmonically to their
nearest neighbors has a Hamiltonian of the form
1 2 N pl
1 2N
H 
 k  (ql  ql 1 ) 2
2 i  0 2m 2 i  0
4. Show that the entropy for Bose-Einstein and Fermi-Dirac gas(neglecting spin) can
be written in the form S  k b  ( n pl ln n pl  1  n pl
i 0
ln( 1  n pl )) where the
top sign hold for Bose-Einstein particles and the bottom sign holds for Fermi-Dirac