**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,
inertial 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. Gyroscope.

**2. Special Relativity, Waves &
Geometrical Optics**

**(a) Special Relativity **:
Michelson-Morley experiment and its
implications. Lorentz transformationslength
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.

**(b) Waves** :
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**:

**(a) Interference**:
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.

**(b) Diffraction**:
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 and Poisson equations in electrostatics
and their applications. Energy
of a system of charges, multiple expansion
of scalar potential. Method of
images1 and its applications. Potential
and field due to a dipole, force and
torque on a dipole in an external field.
Dielectrics, polarisation. Solutions to
boundary-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
equations. Wave equations in vacuum,
Pointing 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**

**(a) Thremodynamics**:
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 gases.

**(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.

**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. LS
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 neutrinos.

**(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 superconductivity.

**6. Electronics **:
Intrinsic and extrinsic semiconductorsp-
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
digital computers.