Obtain expression for average energy for the canonical ensemble in terms of partition function Z.
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A proton inside a nucleus
may have speed upto
. How many quantum states are available to it?
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.
State and prove quantum Liouville equation.
A monthly demand for commodity is a continuous random distribution with probability distribution function given as:
where N is normalization constant. Obtain the value of N so that the function is normalized and hence, find the mean and the variance.
For the grand canonical ensemble, obtain an expression for the ensemble average energy and ensemble average particle numbers.
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.