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.
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Obtain expression for average energy for the canonical ensemble in terms of partition function Z.
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.
The time evolution of the quantum state, is given by the Schrödinger wave equation:
The Hamiltonian for the non-relativistic, non-interacting, monoatomic ideal gas is given by
where m is the mass of the particle and U(qi) is the potential energy. Obtain an expression of the phase space volume of the energy shell and hence obtain an expression of number of microstates.
Using entropy as a function of temperature and pressure, obtain the first Ehrenfest’s equation.
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.
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?