problem 1:

a) State and describe the Hamilton’s principle.
b) Hence or else derive Hamilton’s equations of motion for a system of particles. Describe superiority of such equations over Lagrange’s equations.

problem 2:

a) State and describe principle of least action.
b) Define cyclic coordinates with an illustration and relate them to the conservation theorems.

problem 3:

a) State and describe the postulates of special theory of relativity.
b) Arrive at the Lorentz transformations and mention some effects of the Lorentz transformations.

problem 4:

a) Outline Hamilton-Jacobi theory.
b) Give the importance of Hamilton's principle and characteristic functions. What are Lagrange's Brackets?

problem 5:

a) Give the notion of an ensemble with various types and illustrations.
b) What is Gibb’s paradox? How do you resolve it?

problem 6:

a) From the concept of micro canonical ensemble, derive different thermodynamic parametersof an ideal gas.
b) State and describe the Boltzmann equipartition theorem.

problem 7:

a) State and describe the postulates of quantum statistical mechanics.
b) Describe partition function and its importance in statistical mechanics.

problem 8:

a) What are photons and phonons? Do they obey B – E or F – D statistics? Validate your answer.
b) Describe Bose-Einstein condensation.

problem 9: Answer any two of the given:

a) Inertia tensor and moment of inertia.
b) Normal modes and frequencies of a linear tri-atomic molecule.
c) White dwarf stars.
d) D’ Alembert’s principle and Lagrange’s equations of motion.