Show that the probability that a state with energy above the Fermi level
filled is equal to the probability of a state with energy
below the Fermi level
is empty.
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For the grand canonical ensemble, obtain an expression for the ensemble average energy and ensemble average particle numbers.
State and prove quantum Liouville equation.
What is the Bose-Einstein condensation? Write an expression of number of particles in the excited state (Nex) in terms of Bose-Einstein condensation temperature (Tc), total number of bosons (N) in an assembly and temperature T. Show a plot of distribution of bosons as a function of temperature below and above the Tc.
Using the relation of thermodynamic probability
Obtain an expression of Fermi Dirac distribution function. Show a plot of (the occupation index of a state corresponding to energy
) versus
for different temperatures and discuss it. What is the physical interpretation of Fermi energy?
N particles obey Maxwell-Boltzmann distribution. They are distributed among three states with energies and
. If the equilibrium energy of the system is approximately 3000kBT, calculate the total number of particles.
Show that the probability that a state with energy above the Fermi level
filled is equal to the probability of a state with energy
below the Fermi level
is empty.
What is meant by Cluster Integrals? Express B2 and B3 in terms of Cluster Integrals.