Using entropy as a function of temperature and pressure, obtain the first Ehrenfest’s equation.
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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.
The time evolution of the quantum state, is given by the Schrödinger wave equation:
where H is the Hamiltonian operator. Using this equation, obtain time evolution of the wave function when the energy eigenvalue is E.
Discuss the concept of thermodynamic fluctuations in the canonical ensemble. Define energy fluctuations and derive an expression for the mean square fluctuation of energy. Using a classical ideal gas, show that the relative fluctuation in energy varies as and hence, justify why thermodynamic calculations are valid for ordinary macroscopic systems.
btain the phase space area enclosed by a classical harmonic oscillator for energies ranging from 0 to E.
What is meant by Cluster Integrals? Express B2 and B3 in terms of Cluster Integrals.
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.
State and prove quantum Liouville equation.