GATE APTITUDE 2021 Syllabus
Verbal Aptitude
English grammar
Sentence completion
Instructions
Verbal analogies
Word groups
Critical reasoning
Verbal deduction
Numerical computation
Numerical reasoning
Numerical estimation
Data interpretation
GATE PHYSICS 2021 Syllabus
Mathematical Physics
Linear vector space
basis, orthogonality and completeness
matrices
vector calculus
linear differential equations
elements of complex analysis
Cauchy Riemann conditions, Cauchy's theorems, singularities, residue theorem and applications.
Laplace transforms, Fourier analysis
elementary ideas about tensors: covariant and contravariant tensor, Levi-Civita and Christoffel symbols
Classical Mechanics
Alembert's principle, cyclic coordinates, variational principle
Lagrange'[]s equation of motion, central force and scattering problems, rigid body motion; small oscillations
Hamilton's formalisms; Poisson bracket; special theory of relativity
Lorentz transformations, relativistic kinematics, mass-energy equivalence.
Electromagnetic Theory
Solutions of electrostatic and magnetostatic problems including boundary value problems
dielectrics and conductors
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
Postulates of quantum mechanics
uncertainty principle
Schrodinger equation
one two and three-dimensional potential problems
particle in a box, transmission through one-dimensional potential barriers, harmonic oscillator, hydrogen atom
inear 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, ensemble
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, phase equilibria, 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
rotational and vibrational spectra of diatomic molecules
electronic transition in diatomic molecules
Franck-Condon principle
Raman effect
NMR, ESR, X-ray spectra
lasers: Einstein coefficients, population inversion, two and three-level systems.
Solid State Physics
Elements of crystallography
diffraction methods for structure determination
bonding in solids
lattice vibrations and thermal properties of solids
free electron theory
band theory of solids: nearly free electron and tight-binding models
metals, semiconductors and insulators
conductivity, mobility and effective mass
Optical properties of solids
Kramers-Kronig relation, intra- and inter-band transitions
dielectric properties of solid
dielectric function, polarizability, ferroelectricity
magnetic properties of solids
dia, para, ferro, antiferro and ferri-magnetism, domains and magnetic anisotropy
superconductivity: Type-I and Type II superconductors, Meissner effect, London equation, BCS Theory, flux quantization.
Electronics
Semiconductors in equilibrium: electron and hole statistics in intrinsic and extrinsic semiconductors
metal-semiconductor junctions
Ohmic and rectifying contacts
PN diodes, bipolar junction transistors, field effect transistors
negative and positive feedback circuits
oscillators, operational amplifiers, active filters
basics of digital logic circuits, combinational and sequential circuits
flip-flops, timers, counters, registers, A/D and D/A conversion.
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.