problem 1:
a) State the D’Alembert’s principle and obtain the Lagrange’s equation from it.
b) State and describe principle of least action.
problem 2:
a) What do you understand by the independent coordinates of a rigid body?
b) Describe the coriots force and its importance.
problem 3:
a) State and describe the basic postulator of spatial theory of relativity and get Lorentz transformations.
b) Describe conanical transformation with illustrations.
problem 4:
a) What do you mean by action angle variable? Describe the use of such variables to the problems of Kepler’s laws.
b) Formulate the theory of small oscillations.
problem 5:
a) State and describe equi-partition theorem.
b) What do you mean by Gibb’s paradox? Describe how it has been resolved.
problem 6:
a) Describe the energy fluctuations in the canonical ensemble.
b) Obtain the equivalence between the canonical ensemble and grand canonical ensemble.
problem 7:
a) Describe the postulate of quantum statistical mechanics.
b) Describe the Darwin–Fowler method for finding out the partition function.
problem 8:
a) Obtain an expression for the internal energy of an ideal Fermi gas.
b) Describe Bose-Einstein condensation.
problem 9: prepare notes on any two of the given:
a) Hamilton’s principle.
b) Canonical invariance.
c) Density punctuations in the grand canonical ensemble.
d) Theory of white-dwarf.