NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (5/9)

Derivation of Special Relativity

•    Fundamental concepts

•    Einstein’s formulation of special relativity

•    The Lorentz transformations

•    Length contraction, Time dilation and simultaneity

•    The velocity addition formulae

•    Three dimensional Lorentz transformations

The Four-Vector Formulation of Special Relativity

•    The four-vector formalism

•    The Lorentz transformations in 4-vectors

•    The Lorentz and Poincare groups

•    The null cone structure

•    Proper time

Applications of Special Relativity

•    Relativistic kinematics

•    The Doppler shift in relativity

•    The Compton effect

•    Particle scattering

•    Binding energy, Particle production and particle decay

Electromagnetism in Special Relativity

•    Review of electromagnetism

•    The electric and magnetic field intensities

•    The electric current

•    Maxwell’s equations and electromagnetic waves

•    The four-vector formulation of Maxwell’s equations



Section-II (4/9)

Lagrange’s Theory of Holonomic and Non-Holonomic Systems

•    Generalized coordinates

•    Holonomic and non-holonomic systems

•    D’Alembert’s principle, D-delta rule

•    Lagrange equations

•    Generalization of Lagrange equations

•    Quasi-coordinates 

•    Lagrange equations in quasi-coordinates

•    First integrals of Lagrange equations of motion

•    Energy integral

•    Lagrange equations for non-holonomic systems with and without Lagrange multipliers

•    Hamilton’s Principle for non-holonomic systems

Hamilton’s Theory

•    Hamilton’s principle

•    Generalized momenta and phase space

•    Hamilton’s equations

•    Ignorable coordinates, Routhian function

•    Derivation of Hamilton’s equations from a variational principle

•    The principle of least action

Canonical Transformations

•    The equations of canonical transformations

•    Examples of canonical transformations

•    The Lagrange and Poisson brackets

•    Equations of motion, Infinitesimal canonical transformations and conservation theorems in the Poisson bracket formulation

Hamilton-Jacobi Theory

•    The Hamilton-Jacobi equation for Hamilton’s principal function

•    The harmonic oscillator problem as an example of the Hamilton-Jacobi method

•    The Hamilton-Jacobi equation for Hamilton’s characteristic function

•    Separation of variables in the Hamilton-Jacobi equation