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Course

CSIR NET / JRF Syllabus

CSIR - UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer - ship Syllabus

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  dynamics-moment  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  relativity-Lorentz 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.  Diracnotation  for  state  vectors.  Motion  in  a  central  potential:  orbital  angular  momentum,  angular  momentum algebra,   spin,   addition   of   angular   momenta;   Hydrogen   atom.   Stern-Gerlach   experiment.   Time-independent  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

PhysicsLaws   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 Runge-Kutta 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

PhysicsFirst-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,   chemicalshift.   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,  semi-empirical  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.

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