Second Paper - Physics.
• Dimensional analysis, Vector algebra and vector calculus, Linear algebra.
• Linear differential equations, Special functions (Hermite, Bessel, Laguerre and Legendre).
• Fourier series, Fourier and Laplace transforms, Elements of complex analysis, Laurent series, poles, residues and
evaluation of integrals.
• Elementary ideas about tensors, Introductory group theory, SU(2), O(3).
• Elements of computational techniques, roots of functions, interpolation, extrapolation, integration by trapezoid and
Simpson's rule, solution of first order differential equations using Runge-Kutta method, Finite difference methods.
• Elementary knowledge of probability theory, random variables, binomial, Poisson and normal distributions.
• Newton's laws. Phase space dynamics; stability analysis.
• Central-force motion, Two-body collisions, scattering in laboratory and center-of-mass frames.
• Rigid body dynamics, moment of inertia tensor; non-inertial frames and pseudo-forces.
• Variational principle, Lagrangian and Hamiltonian formalisms and equations of motion; Poisson brackets and
canonical transformations, Symmetry, invariance and conservation laws, cyclic coordinates; Periodic motion, small oscillations and normal modes.
• Special theory of relativity, Lorentz transformations, relativistic kinematics and mass-energy equivalence.
• Electrostatics: Gauss’ Law and its applications, Laplace and Poisson equations, boundary value problems.
• Magnetostatics: Biot-Savart law, Ampere's theorem, electromagnetic induction.
• Maxwell's equations in free space and linear isotropic media, boundary conditions on fields at interfaces, Scalar
and vector potentials, Gauge invariance.
• Electromagnetic waves in free space, dielectrics and conductors, Reflection and refraction, polarization, Fresnel's
Law, interference, coherence and diffraction, Dispersion relations in plasma, Lorentz invariance of Maxwell's equations.
• Transmission lines and wave-guides, Dynamics of charged particles in static and uniform electromagnetic fields,
Radiation from moving charges, dipoles and retarded potentials.
• Wave-particle duality, Wave functions in coordinate and momentum representations, Commutators and
Heisenberg's uncertainty principle, Matrix representation, Dirac's bra and ket notation.
• Schrodinger equation (time-dependent and time-independent), Eigenvalue problems such as particle-in-a-box,
Harmonic oscillator, Tunneling through a barrier.
• Motion in a central potential, Orbital angular momentum, Angular momentum algebra, spin, Addition of angular
momenta, Hydrogen atom, spin-orbit coupling and fine structure.
• Time Independent perturbation theory and its applications, Variational method, WKB approximation.
• Time dependent perturbation theory and Fermi's Golden Rule, Selection rules, Semi-classical theory of radiation,
Elementary theory of scattering, phase shifts, partial waves, Born approximation, Identical particles, Pauli's exclusion principle, spin-statistics connection, Relativistic quantum mechanics, Klein Gordon and Dirac equations.
• Laws of thermodynamics and their consequences, Thermodynamic potentials, Maxwell relations, Chemical
potential, phase equilibria, Phase space, micro and macrostates.
• Microcanonical, canonical and grand-canonical ensembles and partition functions.
• Free energy and connection with thermodynamic quantities, First and second order phase transitions.
• Classical and quantum statistics, ideal Fermi and Bose gases, Blackbody radiation and Planck’s distribution law,
Bose-Einstein condensation.
• Random walk and Brownian motion, Introduction to non-equilibrium processes, Diffusion equation.
• Semiconductor devices including diode, Junction transistors, Field-Effect devices, Homo and Hetero junction
devices.
• Device Structure, device characteristics, Frequency dependence and application.
• Optoelectronic devices including Solar cells, Optical detectors and Light Emitting Diode, High frequency devices
including: generators and detectors.
• Operational amplifier and its application, Digital technique and applications (Registers, Counters, Comparators and
equivalent circuits) Analog to Digital and Digital to Analog Converters, Micro-processor and Micro-controller.
• Data representation and analysis, Analysis of exact and appropriate errors, Propagation of errors.
• Least square fitting, linear and non-linear curve fitting, Chi-square test.
• Transducers (Temperature, Pressure/vacuum, magnetic field, Vibrations, Optical and particle detectors)
measurement and control, Signal conditioning and recovery, impedance matching.
• Amplification (operational amplifier based, instrumentation amplifier, feedback), Filtering and Noise reduction,
shielding and grounding, Fourier transformation.
• Lock-in detector, Box-car integrator, modulation technique.
• Quantum states of an electron in an atom, Electron spin, Stern-Gerlach experiment, Spectrum of Hydrogen, Helium
and alkali atoms.
• Relativistic corrections for energy levels of hydrogen, Hyperfine structure and isotopic shift, width of spectral lines,
LS & JJ coupling.
• Zeeman, Paschen Back & Stark effect, X-ray spectroscopy.
• Electron spin resonance, Nuclear magnetic resonance, chemical shift, Rotational, vibrational, electronic and
Raman spectra of diatomic molecules.
• Frank - Condon principle and selection rules, Spontaneous and stimulated emission, Einstein A & B coefficients,
Lasers, optical pumping, population inversion, rate equation, Modes of resonators and coherence length.
• Bravais lattices, Reciprocal lattice, diffraction and the structure factor.
• Bonding of solids, Elastic properties, phonons, lattice specific heat, free electron theory and electronic specific
heat, Response and relaxation phenomena.
• Drude model of electrical and thermal conductivity, Hall Effect and thermoelectric power. Diamagnetism,
paramagnetism, and ferromagnetism.
• Electron motion in periodic potential, band theory of metals, insulators and semiconductors.
• Superconductivity: Type-I and type II superconductors, Josephson junctions, Defects and dislocations, Ordered
phases of matter, translational and orientational order, kinds of liquid crystalline order, Conducting polymers, Quasicrystals.
• Basic nuclear properties: size, shape, charge distribution, spin and parity, Binding energy. Semi-empirical mass
formula, Liquid drop model, Fission and fusion.
• Nature of the nuclear force, form of nucleon-nucleon potential, Charge-independence and charge-symmetry of
nuclear forces, Isospin; Deuteron problem, Evidence of shell structure, single-particle shell model- its validity and limitations, Rotational spectra.
• Elementary ideas of alpha, beta and gamma decays and their selection rules, nuclear reactions, reaction
mechanisms, compound nuclei and direct reactions.
• Classification of fundamental forces, Elementary particles (quarks, baryons, mesons, leptons), Spin and parity
assignments, isospin, strangeness, Gell-Mann-Nishijima formula; C, P, and T invariance and applications of symmetry arguments to particle reactions, parity non-conservation in weak interaction; Relativistic kinematics.
• Contribution of Aryabhata, Varahmihir, Brahmagupta and Bhaskaracharya to Astrophysics in ancient times. Basic
information of ancient and modern observatories in India. Contribution of Indian Physicists J C Bose, C.V. Raman, S N Bose, Meghnad Saha, Homi Bhabha, Vikram Sarabhai, Raja Ramanna and J. V. Narlikar.
