CSIR-UGC National Eligibility Test (NET) for Junior
Research Fellowship

and Lecturer-ship

PHYSICAL SCIENCES

 P AR T  ‘ 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. 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. 
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 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,

P AR T ‘ 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 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, 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.