GATE 2027 Physics (PH) Syllabus — Revised

Units and dimensions, dimensional analysis; least count, significant figures; methods of measurement and error analysis; 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.

Linear vector spaces: basis, orthogonality, completeness; matrices: similarity transformations, diagonalization, eigenvalues & eigenvectors; linear differential equations (first & second order); complex analysis: Cauchy–Riemann conditions, Cauchy's theorem, singularities, residue theorem; Fourier analysis; tensors: covariant and contravariant tensors.

D'Alembert's principle, Euler–Lagrange equation, Hamilton's principle, calculus of variations; symmetry & conservation laws; central force motion (Kepler); small oscillations, coupled oscillations, normal modes; rigid body dynamics, inertia tensor, Euler angles; Hamiltonian & Hamilton's equations; canonical transformations, Poisson bracket; special relativity: Lorentz transformations, mass-energy equivalence.

Laws of thermodynamics; macrostates & microstates; phase space; ensembles; partition function, free energy; classical & quantum statistics; degenerate Fermi gas; black body radiation, Planck's law; Bose–Einstein condensation; first & second order phase transitions, phase equilibria, critical phenomena.

Electrostatic & magnetostatic boundary value problems; method of images; separation of variables; dielectrics & conductors; magnetic materials; multipole expansion; Maxwell's equations; scalar & vector potentials; Coulomb and Lorentz gauges; EM waves in free space, non-conducting & conducting media; reflection & transmission; polarization; Poynting vector & theorem.

Wave equation, plane & spherical waves, standing waves, phase & group velocity; interference: spatial & temporal coherence, Newton's rings, multiple-beam interference, Michelson & Fabry–Perot interferometers; diffraction: Fresnel & Fraunhofer, rectangular & circular aperture, Rayleigh criterion, double slit, many slits, grating dispersion; polarization: Jones vectors & matrices, birefringence, ray-transfer matrices; lasers: Einstein coefficients, population inversion, 2- and 3-level laser systems.

Basic ideas; uncertainty principle; linear operators in Hilbert space; time-independent Schrödinger equation; 1D potentials: step, finite rectangular well, tunnelling, particle in 1/2/3-D box, delta-function potentials, 1/2/3-D harmonic oscillator, degeneracy; central potentials, hydrogen-like atoms; orbital & spin angular momenta; addition of angular momenta; variational method, time-independent perturbation theory; elementary scattering, Born approximation.

Spectra of one- and many-electron atoms; spin-orbit interaction; LS and jj coupling; 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, Franck–Condon principle; Raman effect and Raman spectroscopy; NMR, ESR, X-ray and Mössbauer spectroscopies.

Elements of crystallography; diffraction methods; bonding in solids; lattice vibrations & thermal properties; free electron theory; band theory: nearly free electron model; metals, semiconductors, insulators; carrier statistics, mobility, effective mass; metal-semiconductor junctions, ohmic & rectifying contacts; dielectric properties, polarizability, ferroelectricity; magnetic properties: dia, para, ferro, antiferro, ferri magnetism; superconductivity: Type-I/II, Meissner effect, London equation, BCS theory, flux quantization.

Nuclear binding energy, electric & magnetic moments; semi-empirical mass formula; nuclear models: liquid drop, shell model; nuclear force & two-nucleon problem; alpha, beta decay, EM transitions; Rutherford scattering, nuclear reactions, conservation laws; fission & fusion; accelerators & detectors; elementary particles: photons, baryons, mesons, leptons; quark model; isospin, C, P, T invariance.

p-n diodes, BJT, FET; negative & positive feedback circuits; oscillators; op-amps & applications; active filters; waveform generators; basics of digital logic; combinational & sequential circuits; flip-flops, timers, counters, registers; A/D and D/A conversion.