1. Classical Mechanics
(a) Particle dynamics
Centre of mass and laboratory coordinates, conservation of linear and
angular momentum. The rocket equation. Rutherford scattering, Galilean
transformation, intertial and non-inertial frames, rotating frames,
centrifugal and Coriolis forces, Foucault pendulum.
(b) System of particles
Constraints, degrees of freedom, generalised coordinates and momenta.
Lagrange's equation and applications to linear harmonic oscillator, simple
pendulum and central force problems. Cyclic coordinates, Hamilitonian
Lagrange's equation from Hamilton's principle.
(c) Rigid body dynamics
Eulerian angles, inertia tensor, principal moments of inertia. Euler's
equation of motion of a rigid body, force-free motion of a rigid body.
2. Special Relativity, Waves & Geometrical Optics
(a) Special Relativity
Michelson-Morley experiment and its implications. Lorentz
transformations-length contraction, time dilation, addition of velocities,
aberration and Doppler effect, mass-energy relation, simple applications to a
decay process. Minkowski diagram, four dimensional momentum vector. Covariance
of equations of physics.
Simple harmonic motion, damped oscillation, forced oscillation and
resonance. Beats. Stationary waves in a string. Pulses and wave packets. Phase
and group velocities. Reflection and Refraction from Huygens' principle.
(c) Geometrical Optics
Laws of relfection and refraction from Fermat's principle. Matrix method
in paraxial optic-thin lens formula, nodal planes, system of two thin lenses,
chromatic and spherical aberrations.
3. Physical Optics
Interference of light-Young's experiment, Newton's rings, interference by
thin films, Michelson interferometer. Multiple beam interference and
Fabry-Perot interferometer. Holography and simple applications.
Fraunhofer diffraction-single slit, double slit, diffraction grating,
resolving power. Fresnel diffraction: - half-period zones and zones plates.
Fresnel integrals. Application of Cornu's spiral to the analysis of
diffraction at a straight edge and by a long narrow slit. Diffraction by a
circular aperture and the Airy pattern.
(c) Polarisation and Modern Optics
Production and detection of linearly and circularly polarised light.
Double refraction, quarter wave plate. Optical activity. Principles of fibre
optics attenuation; pulse dispersion in step index and parabolic index fibres;
material dispersion, single mode fibres. Lasers-Einstein A and B coefficients.
Ruby and He-Ne lasers. Characteristics of laser light-spatial and temporal
coherence. Focussing of laser beams. Three-level scheme for laser operation.
4. Electricity and Magnetism
(a) Electrostatics and Magnetostatics
Laplace ad Poisson equations in electrostatics and their applications.
Energy of a system of charges, multipole expansion of scalar potential. Method
of images and its applications. Potential and field due to a dipole, force and
torque on a dipole in an external field. Dielectrics, polarisation. Solutions
to bounary-value problems-conducting and dielectric spheres in a uniform
electric field. Magentic shell, uniformly magnetised sphere. Ferromagnetic
materials, hysteresis, energy loss.
(b) Current Electricity
Kirchhoff's laws and their applications. Biot-Savart law, Ampere's law,
Faraday's law, Lenz' law. Self-and mutual-inductances. Mean and rms values in
AC circuits. LR CR and LCR circuits- series and parallel resonance. Quality
factor. Principal of transformer.
5. Electromagnetic Theory & Black Body Radiation
(a) Electromagnetic Theory
Displacement current and Maxwell's equatons. Wave equations in vacuum,
Poynting theorem. Vector and scalar potentials. Gauge invariance, Lorentz and
Coulomb gauges. Electromagnetic field tensor, covariance of Maxwell's
equations. Wave equations in isotropic dielectrics, reflection and refraction
at the boundary of two dielectrics. Fresnel's relations. Normal and anomalous
dispersion. Rayleigh scattering.
(b) Blackbody radiation
Balckbody radiation ad Planck radiation law- Stefan-Boltzmann law, Wien
displacement law and Rayleigh-Jeans law. Planck mass, Planck length, Planck
time,. Planck temperature and Planck energy.
6. Thermal and Statistical Physics
Laws of thermodynamics, reversible and irreversible processes, entropy.
Isothermal, adiabatic, isobaric, isochoric processes and entropy change. Otto
and Diesel engines, Gibbs' phase rule and chemical potential. van der Waals
equation of state of a real gas, critical constants. Maxwell-Boltzman
distribution of molecular velocities, transport phenomena, equipartition and
virial theorems. Dulong-Petit, Einstein, and Debye's theories of specific heat
of solids. Maxwell lllrelations and applications. Clausius- Clapeyron
equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of
(b) Statistical Physics
Saha ionization formula. Bose-Einstein condenssation. Thermodynamic
behaviour of an ideal Fermi gas, Chandrasekhar limit, elementary ideas about
neutron stars and pulsars. Brownian motion as a random walk, diffusion
process. Concept of negative temperatures.
Paper-II | Section-A
1. Quantum Mechanics I
Wave-particle dualitiy. Schroedinger equation and expectation values.
Uncertainty principle. Solutions of the one-dimensional Schroedinger equation
free particle (Gaussian wave-packet), particle in a box, particle in a finite
well, linear harmonic oscillator. Reflection and transmission by a potential
step and by a rectangular barrier. Use of WKB formula for the life-time
calcuation in the alpha-decay problem.
2. Quantum Mechanics II & Atomic Physics
(a) Quantum Mechanics II
Particle in a three dimensional box, density of states, free electron
theory of metals. The angular meomentum problem. The hydrogen atom. The spin
half problem and properties of Pauli spin matrices.
(b) Atomic Physics
Stern-Gerlack experiment, electron spin, fine structure of hydrogen atom.
L-S coupling, J-J coupling. Spectroscopic notation of atomic states. Zeeman
effect. Frank-Condon principle and applications.
3. Molecular Physics
Elementary theory of rotational, vibratonal and electronic spectra of
diatomic molecules. Raman effect and molecular structure. Laser Raman
spectroscopy Importance of neutral hydrogen atom, molecular hydrogen and
molecular hydrogen ion in astronomy Fluorescence and Phosphorescence.
Elementary theory and applications of NMR. Elementary ideas about Lamb shift
and its significance.
4. Nuclear Physics
Basic nuclear properties-size, binding energy, angular momentum, parity,
magnetic moment. Semi-empirical mass formula and applications. Mass parabolas.
Ground state of a deuteron magnetic moment and non-central forces. Meson
theory of nuclear forces. Salient features of nuclear forces. Shell model of
the nucleus-success and limitations. Violation of parity in beta decay. Gamma
decay and internal conversion. Elementary ideas about Mossbauer spectroscopy.
Q-value of nuclear reactions. Nuclear fission and fusion, energy production in
stars. Nuclear reactors.
5. Particle Physics & Solid State Physics
(a) Particle Physics
Classification of elementary particles and their interactions. Conservation
laws. Quark structure of hadrons. Field quanta of electroweak and strong
interactions. Elementary ideas about Unification of Forces. Physics of
(b) Solid State Physics
Cubic crystal structure. Band theory of solids- conductors, insulators and
semiconductors. Elements of superconductivity, Meissner effect, Josephson
junctions and applications. Elementary ideas about high temperature
Intrinsic and extrinsic semiconductors-p-n-p and n-p-n transistors.Amplifiers
and oscillators. Op-amps. FET, JFET and MOSFET. Digital electronics-Boolean
identities, De; Morgan's laws, Logic gates and truth tables., Simple logic
circuits. Thermistors, solar cells. Fundamentals of microprocessors and