GATE 2027 IIT Madras | Organizing Institute
PH Physics
Section 1: Measurements and Error Analysis
Units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and
error analysis for physical quantities associated with various measurements; 2-probe and 4-probe methods for
resistance measurement; Grounding for electrical circuits, Ground loops; Design of DC power supply, Signal
processing through lock-in amplifiers.
Section 2: Mathematical Physics
Linear vector spaces: basis, orthogonality and completeness; matrices: similarity transformations,
diagonalization, eigenvalues and eigen vectors; linear differential equations: simple applications of first and
second order linear differential equations and solutions; complex analysis: Cauchy-Riemann conditions,
Cauchy's theorem, singularities, residue theorem and applications; Fourier analysis; tensors: tensor
transformations, covariant and contravariant tensors.
Section 3: Classical Mechanics
D'Alembert's principle, Euler-Lagrange equation, Hamilton's principle, calculus of variations; symmetry and
conservation laws; central force motion: Kepler problem; small oscillations: coupled oscillations and normal
modes; rigid body dynamics: inertia tensor, orthogonal transformations, Euler angles, torque free motion of
a symmetric top; Hamiltonian and Hamilton's equations of motion; canonical transformations: Poisson
bracket. Special theory of relativity: Lorentz transformations, relativistic kinematics, mass-energy
equivalence.
Section 4: Thermodynamics and Statistical Mechanics
Laws of thermodynamics; macrostates and microstates; phase space; 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, phase equilibria, critical phenomena.
Section 5: Electromagnetic theory
Solutions of electrostatic and magnetostatic problems including boundary value problems; method of images;
separation of variables; dielectrics and conductors; magnetic materials; multipole expansion; Maxwell's
equations; scalar and vector potentials; Coulomb and Lorentz gauges; electromagnetic waves in free space,
non-conducting and conducting media; reflection and transmission at normal and oblique incidences;
polarization of electromagnetic waves; Poynting vector, Poynting theorem, energy and momentum of
electromagnetic waves.
Section 6: Optical Physics
Wave equation: plane and spherical waves, superposition of waves, standing waves, phase and group
velocities; Interference: spatial and temporal coherence, dielectric films, Newton’s ring, multiple-beam
interference, Michelson interferometer, Fabry-Perot interferometer and etalon; diffraction: Fresnel and
Fraunhofer diffraction, rectangular and circular aperture, Rayleigh criterion of resolution, diffraction from
double slit and many slits. dispersion by a grating; polarization: Jones vectors and matrices for linear, circular
and elliptical polarization, birefringence, ray-transfer matrix for mirrors and lenses; lasers: Einstein
coefficients, population inversion, two and three level laser systems.
Section 7: Quantum Mechanics
Basic ideas of quantum mechanics; uncertainty principle; linear vectors and operators in Hilbert space; time
independent Schrodinger equation; one dimensional potentials: step potential, finite rectangular well,
tunnelling from a potential barrier, particle in 1,2,3-dimensional box, particle in single and double delta
function potentials, 1,2,3 dimensional harmonic oscillator: concept of degeneracy; central potentials;
GATE 2027 IIT Madras | Organizing Institute
hydrogen-like atoms; orbital and spin angular momenta; addition of angular momenta; variational method,
time independent perturbation theory; elementary scattering theory, Born approximation.
Section 8: Atomic and Molecular Physics
Spectra of one-and many-electron atoms; spin-orbit interaction: L-S and j-j coupling schemes; fine and
hyperfine structures; Zeeman, Paschen-Back and Stark effects; electric dipole transitions and selection rules;
rotational and vibrational spectra of diatomic molecules; electronic transitions in diatomic molecules, FranckCondon principle; Raman effect and basics of Raman spectroscopy; NMR, ESR, X-ray and Mossbauer
spectroscopies.
Section 9: 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
model; metals, semiconductors and insulators; conductivity, electron and hole statistics in intrinsic and
extrinsic semiconductors, mobility and effective mass; metal-semiconductor junctions; ohmic and rectifying
contacts; dielectric properties of solids; polarizability, ferroelectricity; magnetic properties of solids; dia,
para, ferro, antiferro and ferri magnetism, ferromagnetic domains; superconductivity: type-I and type II
superconductors, Meissner effect, London equation, BCS theory, flux quantization.
Section 10: Nuclear and Particle Physics
Nuclear binding energy, electric and magnetic moments; semi-empirical mass formula; nuclear models;
liquid drop model, 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; conservation laws, isospin symmetry, charge conjugation, parity and time-reversal invariance.
Section 11: Electronics
p-n diodes, bipolar junction transistors, field effect transistors; negative and positive feedback circuits;
oscillators, operational amplifiers and their applications, active filters; wave form generators: sine wave,
square wave and triangular wave; basics of digital logic circuits, combinational and sequential circuits, flipflops, timers, counters, registers, A/D and D/A conversion.
https://gate2027.iitm.ac.in/static/doc/GATE2027_Syllabus/PH_GATE2027_Syllabus.pdf
