PATTERN
The Examination is carried out as ONLINE Computer Based Test (CBT) where the candidates will be shown the questions in a random sequence on a computer screen. The duration of the examination will be 3 hours. The medium for all the test papers will be English only.
SYLLABUS
Mathematical Methods
Calculus of single and multiple real variables. Fourier and Laplace transforms. Vector Calculus, Divergence theorem, Green’s theorem, Stokes’ theorem. First order and linear second order differential equations with constant coefficients. Matrices and determinants. Complex numbers.
Mechanics and General Properties of Matter
Newton’s laws of motion and applications. Motion under a central force, and Kepler’s laws. Elastic and inelastic collisions. Rigid body motion. Principal moments and axes. Kinematics of fluids. ernoulli’s theorem.
Oscillations, Waves and Optics
Simple harmonic motion. Damped and forced oscillators. Resonance. Wave equation. Group and phase velocities. Sound waves in media. Doppler Effect. Interference and diffraction. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double refraction and optical rotation.
Electromagnetism
Coulomb’s law. Gauss’s law. Electric field and potential. Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics. Electrostatic energy. Biot-Savart law, Ampere’s law, Faraday’s law of electromagnetic induction. LCR circuits. Maxwell’s equations and plane electromagnetic waves, Poynting’s theorem. Transmission and reflection coefficients (normal incidence only). Lorentz Force and motion of charged particles in electric and magnetic fields.
Thermal and Statistical Physics
Maxwell-Boltzmann distribution. Equipartition of energy. Ideal gas law. Specific heat. van-der-Waals gas and equation of state. Laws of thermodynamics. First law and its consequences. Isothermal and adiabatic processes. Second law and entropy. Maxwell’s thermodynamic relations. Thermodynamic potentials. Fermi-Dirac and Bose-Einstein distributions.
Modern Physics
Basics of special relativity. Length contraction. Time dilation. Relativistic velocity addition theorem. Mass-energy equivalence. Blackbody radiation. Photoelectric effect. Compton effect. Bohr’s atomic model. Pauli exclusion principle. Wave-particle duality. Uncertainty principle. Superposition principle. Schrodinger equation. Particle in a box problem in one, two and three dimensions. Solution of the Schrodinger equation for one dimensional harmonic oscillator. Structure of atomic nucleus, mass and binding energy. Radioactivity.
Solid State Physics, Devices and Electronics
Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg's law. Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. p-n junction diode, I-V characteristics, Zener diode and its applications. Transistor characteristics. R-C coupled amplifiers. Operational Amplifiers: Inverting and non-inverting amplifier. Boolean algebra: Binary number systems; binary addition and subtraction. Conversion from one number system to another. Logic Gates AND, OR, NOT, NAND, NOR, X-OR. Truth tables. Combination of gates.
The Examination is carried out as ONLINE Computer Based Test (CBT) where the candidates will be shown the questions in a random sequence on a computer screen. The duration of the examination will be 3 hours. The medium for all the test papers will be English only.
SYLLABUS
Linear vector spaces. Eigenvalues and eigenvectors. Linear ordinary differential equations of first & second order. Special functions. Partial differential equations. Green’s function. Fourier and Laplace transforms. Complex analysis: analytic functions, poles and residues, series expansion, and evaluation of integrals.
Lagrangian and Hamiltonian formalism. Equations of motion. Central force problem. Conservation laws. Small oscillations and normal modes. Special theory of relativity.
Gauss’s law. Laplace and Poisson equations, boundary value problems. Ampere's law. Electromagnetic induction. Maxwell's equations. Scalar and vector potentials. Gauge invariance. Conservation laws for electromagnetic fields. Electromagnetic waves in free space. Dielectrics and conductors. Reflection and refraction of electromagnetic waves. Dynamics of charged particles in static and uniform electromagnetic fields.
Wavefunctions and operators. Heisenberg uncertainty principle. Schrodinger equation (time-dependent and time-independent). Eigenvalue problems (particle in a box, harmonic oscillator, hydrogen atom). Tunneling. Orbital and spin angular momenta. Addition of angular momenta. Time-independent perturbation theory. Variational method. Time dependent perturbation theory: Fermi's golden rule and selection rules. Identical particles and indistinguishability.
Laws of thermodynamics and their consequences. Thermodynamic potentials. Legendre transformation. Maxwell relations. Chemical potential, phase equilibria. Micro-canonical, canonical and grandcanonical ensembles and partition functions. Free energy and its connection with thermodynamic quantities. Classical and quantum statistics. Ideal Bose and Fermi gases. Blackbody radiation and Planck's distribution. First- and second-order phase transitions.
Quantum states of electrons in an atom. Relativistic corrections of atomic energy levels. LS & JJ couplings. Zeeman, Paschen-Bach & Stark effects. Magnetic resonance. Born-Oppenheimer approximation. Electronic, rotational, vibrational and Raman spectra of diatomic molecules. Lasers: spontaneous and stimulated emission, Einstein A & B coefficients. Optical pumping, population inversion, rate equation.
Bravais lattices. Reciprocal lattice. Diffraction and structure factor. Bonding of solids. Elastic properties, phonons, lattice specific heat. Free electron theory of metals and electronic specific heat. Drude model of electrical and thermal conductivity. Hall effect and thermoelectric power. Band theory of solids: metals, insulators and semiconductors. Superconductivity: type-I and type-II superconductors. Magnetism: types of magnetic ordering and Curie-Weiss law.
Basic nuclear properties: size, shape and charge distribution, spin and parity. Binding energy, semi-empirical mass formula, liquid drop model. Nuclear force. Single-particle shell model, its validity and limitations. Rotational spectra. Elementary ideas of alpha, beta and gamma decays and their selection rules. Fission and fusion. Nuclear reactions.
Classification of fundamental forces. Elementary particles and their quantum numbers (charge, spin, parity, isospin, strangeness, etc.).
Semiconductor devices (diodes, junctions, transistors, and field effect devices), device characteristics. Operational amplifiers and their applications. Digital techniques and applications (registers, counters, comparators and similar circuits).
Data analysis. Error estimation. Measurement of electrical resistivity, Hall coefficient, magnetic susceptibility and thermal conductivity. Interference and diffraction experiments. Spectroscopic measurements such as Zeeman effect, Electron Spin Resonance, and Raman effect. Experimental determination of fundamental constants such as Planck’sconstant, e/m, and Boltzmann constant.