Download A system consist of two particles,each of which has two possible

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
if:
(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
2
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
particles.