Download Syllabus - Physics (PH)- IIT-JAM 2017

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Syllabus - Physics (PH)- IIT-JAM 2017
Mathematical Methods: Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect
and perfect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus, Multiple
integrals, Divergence theorem, Green’s theorem, Stokes’ theorem. First order equations and linear second
order differential equations with constant coefficients. Matrices and determinants, Algebra of complex
numbers.
Mechanics and General Properties of Matter: Newton’s laws of motion and applications, Velocity and
acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal
and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field,
Conservative and non-conservative forces. System of particles, Center of mass, equation of motion of the
CM, conservation of linear and angular momentum, conservation of energy, variable mass systems.
Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments
of Inertia and products of Inertia, parallel and perpendicular axes theorem. Principal moments and axes.
Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem.
Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general
solution. Super¬position of two or more simple harmonic oscillators. Lissajous figures. Damped and
forced oscillators, resonance. Wave equation, traveling and standing waves in one-dimension. Energy
density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media.
Doppler Effect. Fermat’s Principle. General theory of image formation. Thick lens, thin lens and lens
combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and
resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double
refraction and optical rotation.
Electricity and Magnetism: Coulomb’s law, Gauss’s law. Electric field and potential. Electrostatic
boundary conditions, Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics,
dielectric polarization, volume and surface charges, electrostatic energy. Biot-Savart law, Ampere’s law,
Faraday’s law of electromagnetic induction, Self and mutual inductance. Alternating currents. Simple DC
and AC circuits with R, L and C components. Displacement current, Maxwell’s equations and plane
electromagnetic waves, Poynting’s theorem, reflection and refraction at a dielectric interface, transmission
and reflection coefficients (normal incidence only). Lorentz Force and motion of charged particles in
electric and magnetic fields.
Kinetic theory, Thermodynamics: Elements of Kinetic theory of gases. Velocity distribution and
Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas
and equation of state. Mean free path. Laws of thermodynamics. Zeroth law and concept of thermal
equilibrium. First law and its consequences. Isothermal and adiabatic processes. Reversible, irreversible
and quasi-static processes. Second law and entropy. Carnot cycle. Maxwell’s thermodynamic relations
and simple applications. Thermodynamic potentials and their applications. Phase transitions and ClausiusClapeyron equation. Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein
distributions.
Modern Physics: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz
transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy
equivalence. Blackbody radiation, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays.
Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation
values, Schrödinger equation and its solution for one, two and three dimensional boxes. Solution of
Schrödinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step
potential, Pauli exclusion principle. ??????????? ???? ??????????? ?????? ??????? ??????.
Radioactivity and its applications. Laws of radioactive decay.
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,
BJT: characteristics in CB, CE, CC modes. Single stage amplifier, two stage R-C coupled amplifiers.
Simple Oscillators: Barkhausen condition, sinusoidal oscillators. OPAMP and applications: Inverting and
non-inverting amplifier. Boolean algebra: Binary number systems; conversion from one system to another
system; binary addition and subtraction. Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth
tables; combination of gates; de Morgan’s theorem.
JEST-2015
Syllabus for Physics
Mathematical Methods
Vector algebra and vector calculus; linear vector spaces, linear operators, matrices and Eigen
value problem; Sturm–Liouville theory, classical orthogonal polynomials; linear ordinary
differential equations, exact and series methods of solution; linear partial differential
equations, solution by separation of variables; complex variables, analytic functions, Taylor
and Laurent expansions, contour integration; Fourier and Laplace transforms.
Classical Mechanics
Newton’s laws, conservation of energy and momentum, collisions; generalized coordinates,
principle of least action, Lagrangian and Hamiltonian formulations of mechanics; symmetry
and conservation laws; central force problem, Kepler problem; rigid body motion; small
oscillations and normal modes; special relativity in classical mechanics.
The uncertainty principle; conceptual basis of quantum mechanics; Schrodinger equation,
problems in one, two and three dimensions, bound states and tunnelling, particle in a box,
harmonic oscillator, hydrogen atom; matrix formulation of quantum theory, unitary
transformations and Hermitian operators and their properties; orbital and spin angular
momenta, addition of angular momenta; time independent and time dependent perturbation
theory, Fermi golden rule; elementary scattering theory.
Electromagnetic Theory
Laws of electrostatics and magnetostatics, methods of solving boundary value problems,
multipole expansion; fields in conducting, dielectric, diamagnetic and paramagnetic
materials; Faraday’s law and time varying fields; conservation of charge, displacement
current; Maxwell’s equations; energy and momentum of electromagnetic fields, Poynting
theorem; propagation of plane electromagnetic waves, reflection and refraction of plane
electromagnetic waves, electromagnetic waves in dispersive and conducting media; scalar
and vector potentials, Coulomb and Lorentz gauge, wave equation in terms of
electromagnetic potentials; radiation from moving charges, retarded and advanced potentials,
Lienard-Wiechert potentials, multipole radiation, Larmor’s formula.
Quantum Mechanics
The uncertainty principle; conceptual basis of quantum mechanics; Schrodinger equation,
problems in one, two and three dimensions, bound states and tunnelling, particle in a box,
harmonic oscillator, hydrogen atom; matrix formulation of quantum theory, unitary
transformations and Hermitian operators and their properties; orbital and spin angular
momenta, addition of angular momenta; time independent and time dependent perturbation
theory, Fermi golden rule; elementary scattering theory
1
Thermodynamics and Statistical Physics
Laws of thermodynamics; work and heat; thermodynamic potentials, Maxwell’s relations;
statistical ensembles; partition function; classical ideal gas, harmonic oscillators; classical
and quantum statistics; Fermi and Bose gases; black body radiation; first and second order
phase transitions.
Solid State Physics
Simple crystal structures and X-ray diffraction; lattice vibrations and thermal properties of
solids; free electron theory; band theory of solids; metals, semiconductors and insulators;
basic electrical, optical and magnetic properties of solids; elements of superconductivity.
Electronics
Diodes, rectifier circuits, junctions, transistors and field effect devices; device characteristics,
frequency dependence and applications like active filters and oscillator circuits; solar cells,
photo detectors, and LEDs; operational amplifiers and their applications; Boolean algebra,
digital techniques and applications: registers, counters, comparators and similar circuits; A/D
and D/A converters; microprocessor and microcontroller basics.
Nuclear and Particle Physics
Structure of the nucleus; binding energy, nuclear fusion and fission; radioactive decay, barrier
penetration by alpha particles; classification of elementary particles and fundamental
interactions, leptons and hadrons, elementary ideas of quark model; conservation laws in
particle reactions.
Atomic and Optical Physics
Interference, diffraction and polarization of light; photoelectric effect; spectra of single and
multiple electron atoms; Zeeman and Stark effects; electric dipole transition and selection
rules; hyperfine structure; spontaneous and stimulated emission. Experimental data and error
analysis
Probability theory
Gaussian and Poisson distributions; error analysis; propagation of errors; significant figures;
least square fitting.
2
Syllabus for Physics (PH)
Mathematical Physics: Linear vector space; matrices; vector calculus; linear differential
equations; elements of complex analysis; Laplace transforms, Fourier analysis, elementary ideas
about tensors.
Classical Mechanics: Conservation laws; central forces, Kepler problem and planetary motion;
collisions and scattering in laboratory and centre of mass frames; mechanics of system of
particles; rigid body dynamics; moment of inertia tensor; noninertial frames and pseudo forces;
variational principle; Lagrange’s and Hamilton’s formalisms; equation of motion, cyclic
coordinates, Poisson bracket; periodic motion, small oscillations, normal modes; special theory
of relativity – Lorentz transformations, relativistic kinematics, mass-energy equivalence.
Electromagnetic Theory: Solution of electrostatic and magnetostatic problems
includingboundary value problems;dielectrics andconductors; Biot-Savart’s and Ampere’s laws;
Faraday’s law; Maxwell’s equations; scalar and vector potentials; Coulomb and Lorentz gauges;
Electromagnetic waves and their reflection, refraction, interference, diffraction and polarization.
Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation
from a moving charge.
Quantum Mechanics: Physical basis of quantum mechanics; uncertainty principle; Schrodinger
equation; one, two and three dimensional potential problems; particle in a box, harmonic
oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and
spin; addition of angular momenta; time independent perturbation theory; elementary scattering
theory.
Thermodynamics and Statistical Physics: Laws of thermodynamics; macrostates and
microstates; phase space; probability ensembles; partition function, free energy, calculation of
thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body
radiation and Planck’s distribution law; Bose-Einstein condensation; first and second order phase
transitions, critical point.
Atomic and Molecular Physics: Spectra of one- and many-electron atoms; LS and jj coupling;
hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; Xray spectra; rotational and vibrational spectra of diatomic molecules; electronic transition in
diatomic molecules, Franck-Condon principle; Raman effect; NMR and ESR; lasers.
Solid State Physics: Elements of crystallography; diffraction methods for structure
determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations
and thermal properties of solids; free electron theory; band theory of solids; metals,
semiconductors and insulators; transport properties; optical, dielectric and magnetic properties of
solids; elements of superconductivity.
Nuclear and Particle Physics: Nuclear radii and charge distributions, nuclear binding energy,
Electric and magnetic moments; nuclear models, liquid drop model – semi-empirical mass
formula, Fermi gas model of nucleus, nuclear shell model; nuclear force and two nucleon
problem; Alpha decay, Beta-decay, electromagnetic transitions in nuclei;Rutherford
scattering,nuclear reactions, conservation laws; fission and fusion;particle accelerators and
detectors; elementary particles, photons, baryons, mesons and leptons; quark model.
Electronics: Network analysis; semiconductor devices; Bipolar Junction Transistors, Field
Effect Transistors, amplifier and oscillator circuits; operational amplifier, negative feedback
circuits ,active filters and oscillators; rectifier circuits, regulated power supplies; basic digital
logic circuits, sequential circuits, flip-flops, counters, registers, A/D and D/A conversion.
CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship
and Lecturer-ship
PHYSICAL SCIENCES
PART ‘A’ CORE
I.
Mathematical Methods of Physics
Dimensional analysis. Vector algebra and vector calculus. Linear algebra, matrices, Cayley-Hamilton
Theorem. Eigenvalues and eigenvectors. Linear ordinary differential equations of first & second order,
Special functions (Hermite, Bessel, Laguerre and Legendre functions). Fourier series, Fourier and Laplace
transforms. Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues
and evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and
normal distributions. Central limit theorem.
II.
Classical Mechanics
Newton’s laws. Dynamical systems, Phase space dynamics, stability analysis. Central force motions.
Two body Collisions - scattering in laboratory and Centre of mass frames. Rigid body dynamicsmoment of inertia tensor. Non-inertial frames and pseudoforces. Variational principle. Generalized
coordinates. Lagrangian and Hamiltonian formalism and equations of motion. Conservation laws and
cyclic coordinates. Periodic motion: small oscillations, normal modes. Special theory of relativityLorentz transformations, relativistic kinematics and mass–energy equivalence.
III. Electromagnetic Theory
Electrostatics: Gauss’s 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 the 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. Dynamics
of charged particles in static and uniform electromagnetic fields.
IV. Quantum Mechanics
Wave-particle duality. Schrödinger equation (time-dependent and time-independent). Eigenvalue
problems (particle in a box, harmonic oscillator, etc.). Tunneling through a barrier. Wave-function in
coordinate and momentum representations. Commutators and Heisenberg uncertainty principle. Dirac
notation for state vectors. Motion in a central potential: orbital angular momentum, angular momentum
algebra, spin, addition of angular momenta; Hydrogen atom. Stern-Gerlach experiment. Timeindependent perturbation theory and applications. Variational method. Time dependent perturbation
theory and Fermi's golden rule, selection rules. Identical particles, Pauli exclusion principle, spin-statistics
connection.
V.
Thermodynamic and Statistical Physics
Laws of thermodynamics and their consequences. Thermodynamic potentials, Maxwell relations,
chemical potential, phase equilibria. Phase space, micro- and macro-states. Micro-canonical, canonical
and grand-canonical ensembles and partition functions. Free energy and its connection with
thermodynamic quantities. Classical and quantum statistics. Ideal Bose and Fermi gases. Principle of
detailed balance. Blackbody radiation and Planck's distribution law.
VI.
Electronics and Experimental Methods
Semiconductor devices (diodes, junctions, transistors, field effect devices, homo- and hetero-junction
devices), device structure, device characteristics, frequency dependence and applications. Opto-electronic
devices (solar cells, photo-detectors, LEDs). Operational amplifiers and their applications. Digital
techniques and applications (registers, counters, comparators and similar circuits). A/D and D/A
converters. Microprocessor and microcontroller basics.
Data interpretation and analysis. Precision and accuracy. Error analysis, propagation of errors. Least
squares fitting,
PART ‘B’ ADVANCED
I.
Mathematical Methods of Physics
Green’s function. Partial differential equations (Laplace, wave and heat equations in two and three
dimensions). Elements of computational techniques: root of functions, interpolation, extrapolation,
integration by trapezoid and Simpson’s rule, Solution of first order differential equation using RungeKutta method. Finite difference methods. Tensors. Introductory group theory: SU(2), O(3).
II. Classical Mechanics
Dynamical systems, Phase space dynamics, stability analysis. Poisson brackets and canonical
transformations. Symmetry, invariance and Noether’s theorem. Hamilton-Jacobi theory.
III. Electromagnetic Theory
Dispersion relations in plasma. Lorentz invariance of Maxwell’s equation. Transmission lines and wave
guides. Radiation- from moving charges and dipoles and retarded potentials.
IV. Quantum Mechanics
Spin-orbit coupling, fine structure. WKB approximation. Elementary theory of scattering: phase shifts,
partial waves, Born approximation. Relativistic quantum mechanics: Klein-Gordon and Dirac equations.
Semi-classical theory of radiation.
V. Thermodynamic and Statistical Physics
First- and second-order phase transitions. Diamagnetism, paramagnetism, and ferromagnetism. Ising
model. Bose-Einstein condensation. Diffusion equation. Random walk and Brownian motion.
Introduction to nonequilibrium processes.
VI.
Electronics and Experimental Methods
Linear and nonlinear curve fitting, chi-square test. Transducers (temperature, pressure/vacuum, magnetic
fields, vibration, optical, and particle detectors). Measurement and control. Signal conditioning and
recovery. Impedance matching, amplification (Op-amp based, instrumentation amp, feedback), filtering
and noise reduction, shielding and grounding. Fourier transforms, lock-in detector, box-car integrator,
modulation techniques.
High frequency devices (including generators and detectors).
VII. Atomic & Molecular Physics
Quantum states of an electron in an atom. Electron spin. Spectrum of helium and alkali atom. Relativistic
corrections for energy levels of hydrogen atom, hyperfine structure and isotopic shift, width of spectrum
lines, LS & JJ couplings. Zeeman, Paschen-Bach & Stark effects. Electron spin resonance. Nuclear
magnetic resonance, chemical shift. Frank-Condon principle. Born-Oppenheimer approximation.
Electronic, rotational, vibrational and Raman spectra of diatomic molecules, selection rules. Lasers:
spontaneous and stimulated emission, Einstein A & B coefficients. Optical pumping, population
inversion, rate equation. Modes of resonators and coherence length.
VIII. Condensed Matter Physics
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. Electron motion in a periodic potential, band theory of solids: metals, insulators
and semiconductors. Superconductivity: type-I and type-II superconductors. Josephson junctions.
Superfluidity. Defects and dislocations. Ordered phases of matter: translational and orientational order,
kinds of liquid crystalline order. Quasi crystals.
IX.
Nuclear and Particle Physics
Basic nuclear properties: size, shape and charge distribution, spin and parity. Binding energy, semiempirical mass formula, liquid drop model. Nature of the nuclear force, form of nucleon-nucleon
potential, charge-independence and charge-symmetry of nuclear forces. 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. Fission and fusion. Nuclear reactions,
reaction mechanism, compound nuclei and direct reactions.
Classification of fundamental forces. Elementary particles and their quantum numbers (charge, spin,
parity, isospin, strangeness, etc.). Gellmann-Nishijima formula. Quark model, baryons and mesons. C, P,
and T invariance. Application of symmetry arguments to particle reactions. Parity non-conservation in
weak interaction. Relativistic kinematics.