PAPER – I
1. Mechanics of Particles:
Laws of motion; conservation of energy and momentum, applications to rotating frames, cent r ipetaland Cor iol is accelerat ions; Motion under a central force; Conservation of angular momentum,Kepler's laws; Fields and potentials; Gravitational field and potential due to spherical bodies, Gaussand Poisson equations, gravitational self-energy; Two-body problem; Reduced mass; Rutherfordscattering; Centre of mass an laboratory reference frames.
Mechanics of Rigid Bodies: System of particles; Centre of mass, angular momentum, equations ofmotion; Conservation theorems for energy, momentum and angular momentum; Elastic and inelasticcollisions; 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.
Mechanics of Continuous Media: Elasticity, Hooke's law and elastic constants of isotropic solids andtheir inter-relation; Streamline (Laminar) flow, viscosity, Poiseuille's equation, Bernoulli's equation,Stokes' law and applications.
Special Relativity: Michelson-Morley experiment and its implications; Lorentz transformations-lengthcontraction, time dilation, addition of relativistic velocities, aberration and Doppler effect, mass-energyrelation, simple applications to a decay process; Four dimensional momentum vector; Covariance ofequations of physics.
2. Waves and Optics: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 andRefraction from Huygens' principle.
Geometrical Optics: Laws of reflection and refraction from Fermat's principle ; Matrix method inparaxial optics-thin lens formula, nodal planes, system of two thin lenses, chromatic and sphericalaberrations.
Interference: Interference of light-Young's experiment, Newton's rings, interference by thin films,Michelson interferometer; Multiple beam interference and Fabry-Perot interferometer.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 zoneplates, circular aperture.
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; Pulsedispersion in step index and parabolic index f ibres; Mater ial dispersion, single mode fibres; Lasers-Einstein A and B coefficients; Ruby and He-Ne lasers; Characteristics of laser light-spatial andtemporal coherence; Focusing of laser beams; Three-level scheme for laser operation; Holography andsimple applications.
3. Electricity and Magnetism:
Electrostatics and Magnetostatics: Laplace and Poisson equations in electrostatics and theirapplications; Energy of a system of charges, multipole expansion of scalar potential; Method of imagesand 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.
Current Electricity: Kirchhoff's laws and their applications; Biot-Savart law, Ampere's law, Faraday'slaw, Lenz' law; Self-and mutual-inductances; Mean and r m s values in AC circuits; DC and AC circuitswith R, L and C components; Series and parallel resonances; Quality factor; Principle of transformer.
Electromagnetic Waves and Blackbody Radiation: Displacement current and Maxwell's equations;Wave equations in vacuum, Poynting theorem; Vector and scalar potentials; Electromagnetic fieldtensor, covariance of Maxwell's equations; Wave equations in isotropic dielectrics, reflection andrefraction at the boundary of two dielectrics; Fresnel's relations; Total internal reflection; Normal andanomalous dispersion; Rayleigh scattering; Blackbody radiation and Planck's radiation law, Stefan -Boltzmann law, Wien's displacement law and Rayleigh-Jeans' law.
4.Thermal and Statistical Physics:
Thermodynamics: Laws of thermodynamics, reversible and irreversible processes, entropy; Isothermal,adiabatic, isobaric, isochoric processes and entropy changes; Otto and Diesel engines, Gibbs' phase ruleand 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-Pet i t , Einstein, and Debye's theories of specific heat of solids; Maxwell relations andapplications ; Clausius- Clapeyron equation; Adiabatic demagnetisation, Joule-Kelvin effect andliquefaction of gases.
Statistical Physics: Macro and micro states, statistical distributions, Maxwell-Boltzmann, Bose-Einsteinand Fermi-Dirac distributions, applications to specific heat of gases and blackbody radiation; Conceptof negative temperatures.
PAPER – II
1. Quantum Mechanics:
Wave-particle dualitiy; Schroedinger equation and expectation values; Uncertainty principle; Solutionsof the one-dimensional Schroedinger equation for a free particle (Gaussian wave-packet), particle in abox, particle in a finite well, linear harmonic oscillator; Reflection and transmission by a step potentialand by a rectangular barrier; Particle in a three dimensional box, density of states, free electron theoryof metals; Angular momentum; Hydrogen atom; Spin half particles, properties of Pauli spin matrices.
2. 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; FrankCondon principle and applications;Elementary theory of rotational, vibratonal and electronic spectra of diatomic molecules; Raman effectand molecular structure; Laser Raman spectroscopy; Importance of neutral hydrogen atom, molecularhydrogen and molecular hydrogen ion in astronomy; Fluorescence and Phosphorescence; Elementarytheory and applications of NMR and EPR; Elementary ideas about Lamb shift and its significance.
3. Nuclear and Particle Physics:
Basic nuclear properties-size, binding energy, angular momentum, parity, magnetic moment; Semi-empirical mass formula and appl icat ions, mass parabolas; Ground state of deuteron, magnetic momentand non-central forces; Meson theory of nuclear forces; Salient features of nuclear forces;Shell modelof the nucleus - successes and limitations; Violation of parity in beta decay; Gamma decay and internalconversion; Elementary ideas about Mossbauer spectroscopy; Q-value of nuclear reactions; Nuclearfission and fusion, energy production in stars; Nuclear reactors.
Classification of elementary particles and their interactions ; Conservation laws ; Quark structure ofhadrons; Field quanta of electroweak and strong interactions; Elementary ideas about unification offorces; Physics of neutrinos.
4. Solid State Physics, Devices and Electronics:
Crystalline and amorphous structure of matter; Different crystal systems, space groups; Methods ofdetermination 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 temperaturesuperconductivity.
Intrinsic and extrinsic semiconductors; pn-p and n-p-n transistors; Amplifiers and osci l lators; Op-amps; FET, JFET and MOSFET; Digital electronics-Boolean identities, De Morgan's laws, logic gatesand truth tables; Simple logic circuits; Thermistors, solar cells; Fundamentals of microprocessors anddigital computers.
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