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.
a) State and describe principle of least action.
b) Define cyclic coordinates with an illustration and relate them to the conservation theorems.
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.
a) Outline Hamilton-Jacobi theory.
b) Give the importance of Hamilton's principle and characteristic functions. What are Lagrange's Brackets?
a) Give the notion of an ensemble with various types and illustrations.
b) What is Gibb’s paradox? How do you resolve it?
a) From the concept of micro canonical ensemble, derive different thermodynamic parametersof an ideal gas.
b) State and describe the Boltzmann equipartition theorem.
a) State and describe the postulates of quantum statistical mechanics.
b) Describe partition function and its importance in statistical mechanics.
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.