Includes classical mechanics, quantum physics, electromagnetism, and thermodynamics, for candidates pursuing physics research or teaching.

GATE Physics

Official 2025 syllabus extracted from https://gate2025.iitr.ac.in/doc/2025/GATE%20_PH_2025_Syllabus.pdf

Mathematical Physics

Linear vector space: basis, orthogonality, completeness

Matrices

Similarity transformations

Diagonalization

Eigen values and eigen vectors

Second order linear differential equations and special functions

Cauchy-Riemann conditions

Cauchy's theorem

Singularities

Residue theorem and applications

Laplace transform

Fourier analysis

Tensors: covariant and contravariant

Classical Mechanics

D'Alembert's principle

Euler-Lagrange equation

Hamilton's principle

Calculus of variations

Symmetry and conservation laws

Central force motion: Kepler problem

Rutherford scattering

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

Liouville's theorem

Canonical transformations: action-angle variables

Poisson brackets

Hamilton-Jacobi equation

Lagrangian Formulation

Lorentz transformations

Relativistic kinematics

Mass-energy equivalence

Special Theory of Relativity

Electromagnetic Theory

Electrostatic and magnetostatic 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

EM waves in free space, non-conducting and conducting media

Reflection and transmission at normal and oblique incidences

Polarization of EM waves

Poynting vector and Poynting theorem

Energy and momentum of EM waves

Radiation from a moving charge

Quantum Mechanics

Postulates of quantum mechanics

Uncertainty principle

Schrodinger equation

Dirac Bra-Ket notation

Linear vectors and operators in Hilbert space

One-dimensional potentials: step, finite well, tunneling

Particle in a box

Harmonic oscillator

Two and three dimensional systems

Concept of degeneracy

Hydrogen atom

Angular momentum and spin

Addition of angular momenta

Variational method

WKB approximation

Time independent perturbation theory

Elementary scattering theory

Born approximation

Symmetries in quantum mechanical systems

Thermodynamics and Statistical Physics

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 point

Atomic and Molecular Physics

Spectra of one- and many-electron atoms

Spin-orbit interaction: LS and jj couplings

Fine and hyperfine structures

Zeeman and Stark effects

Electric dipole transitions and selection rules

Rotational and vibrational spectra of diatomic molecules

Electronic transitions in diatomic molecules

Franck-Condon principle

Raman effect

EPR, NMR, ESR, X-ray spectra

Lasers: Einstein coefficients, population inversion

Two and three level systems

Solid State Physics

Crystallography

Diffraction methods for structure determination

Bonding in solids

Lattice vibrations and thermal properties

Free electron theory

Band theory: 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 function, polarizability, ferroelectricity

Magnetic properties: dia, para, ferro, antiferro, ferri

Domains and magnetic anisotropy

Superconductivity: Type-I and Type-II

Meissner effect

London equation

BCS Theory

Flux quantization

Electronics

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

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

Semi-empirical mass formula

Liquid drop model

Nuclear shell model

Nuclear force and two nucleon problem

Alpha decay

Beta decay

Electromagnetic transitions in nuclei

Nuclear reactions and conservation laws

Fission and fusion

Particle accelerators and detectors

Elementary particles: photons, baryons, mesons, leptons

Quark model

Isospin symmetry

Charge conjugation

Parity and time-reversal invariance

GATE Physics Syllabus 2025, 2026 and more: Subjects, Topics, and What to Study