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.