(a) Mechanics of Particles:
Laws of motion; conservation of energy and momentum, applications
to rotating frames, centripetal and Coriolis accelerations; Motion under
a central force; Conservation of angular momentum, Kepler’s laws;
Fields and potentials; Gravitational field and potential due to spherical
bodies, Gauss and Poisson equations, gravitational self-energy; Two-body
problem; Reduced mass; Rutherford scattering; Centre of mass and laboratory
reference frames. (b) Mechanics of Rigid Bodies: System of particles;
Centre of mass, angular momentum, equations of motion; Conservation
theorems for energy, momentum and angular momentum; Elastic and inelastic
collisions; Rigid body; Degrees of freedom, Euler’s theorem, angular
velocity, angular momentum, moments of inertia, theorems of parallel
and perpendicular axes, equation of motion for rotation; Molecular rotations
(as rigid bodies); Di and tri-atomic molecules; Precessional motion;
top, gyroscope. (c) Mechanics of Continuous Media: Elasticity, Hooke’s
law and elastic constants of isotropic solids and their inter-relation;
Streamline (Laminar) flow, viscosity, Poiseuille’s equation, Bernoulli’s
equation, Stokes’ law and applications. (d) Special Relativity: Michelson-Morley experiment
and its implications; Lorentz transformations-length contraction, time
dilation, addition of relativistic velocities, aberration and Doppler
effect, mass-energy relation, simple applications to a decay process;
Four dimensional momentum vector; Covariance of equations of physics.
Waves and Optics:
(a) 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.
(b) Geometrical Optics: Laws of reflection and refraction from
Fermat's principle; Matrix method in paraxial optics-thin lens formula,
nodal planes, system of two thin lenses, chromatic and spherical aberrations. (c) Interference: Interference of light-Young's experiment,
Newton's rings, interference by thin films, Michelson interferometer;
Multiple beam interference and Fabry-Perot interferometer. (d) Diffraction: Fraunhofer diffraction-single slit,
double slit, diffraction grating, resolving power; Diffraction by a
circular aperture and the Airy pattern; Fresnel diffraction: half-period
zones and zone plates, circular aperture.
(e) Polarization and Modern Optics: Production and detection
of linearly and circularly polarized 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; Focusing of laser beams; Three-level scheme for laser operation;
Holography and simple applications.
Electricity and Magnetism:
(a) Electrostatics and Magnetostatics: Laplace and 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, polarization;
Solutions to boundary-value problems-conducting and dielectric spheres
in a uniform electric field; Magnetic shell, uniformly magnetized 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 r m s values in AC circuits; DC
and AC circuits with R, L and C components; Series and parallel resonances;
Quality factor; Principle of transformer. (c) Electromagnetic Waves and Blackbody Radiation: Displacement
current and Maxwell's equations; Wave equations in vacuum, Poynting
theorem; Vector and scalar potentials; 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; Total internal reflection; Normal and anomalous dispersion;
Rayleigh scattering; Blackbody radiation and Planck’s radiation
law, Stefan-Boltzmann law, Wien’s displacement law and Rayleigh-Jeans’
law.
Thermal and Statistical Physics: (a) Thermodynamics: Laws of thermodynamics, reversible
and irreversible processes, entropy; Isothermal, adiabatic, isobaric,
isochoric processes and entropy changes; 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 relations and applications; Clausius- Clapeyron equation; Adiabatic
demagnetisation, Joule-Kelvin effect and liquefaction of gases. (b) Statistical Physics: Macro and micro states, statistical
distributions, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions,
applications to specific heat of gases and blackbody radiation; Concept
of negative temperatures.
PAPER - II
Quantum Mechanics: Wave-particle dualitiy; Schroedinger
equation and expectation values; Uncertainty principle; Solutions of
the one-dimensional Schroedinger equation for a free particle (Gaussian
wave-packet), particle in a box, particle in a finite well, linear harmonic
oscillator; Reflection and transmission by a step potential and by a
rectangular barrier; Particle in a three dimensional box, density of
states, free electron theory of metals; Angular momentum; Hydrogen atom;
Spin half particles, properties of Pauli spin matrices.
Atomic and Molecular Physics: Stern-Gerlach 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; 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 and EPR;
Elementary ideas about Lamb shift and its significance.
Nuclear and Particle Physics: Basic nuclear properties-size,
binding energy, angular momentum, parity, magnetic moment; Semi-empirical
mass formula and applications, mass parabolas; Ground state of deuteron,
magnetic moment and non-central forces; Meson theory of nuclear forces;
Salient features of nuclear forces; Shell model of the nucleus - successes
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.
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.
Solid State Physics, Devices and Electronics: Crystalline
and amorphous structure of matter; Different crystal systems, space
groups; Methods of determination of crystal structure; X-ray diffraction,
scanning and transmission electron microscopies; Band theory of solids
- conductors, insulators and semiconductors; Thermal properties of solids,
specific heat, Debye theory; Magnetism: dia, para and ferromagnetism;
Elements of superconductivity, Meissner effect, Josephson junctions
and applications; Elementary ideas about high temperature superconductivity.
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 digital computers.
