# (Syllabus) Graduate Aptitude Test in Engineering (GATE) Syllabus | Physics

**Graduate Aptitude Test in Engineering (GATE) Syllabus | Physics**

**Mathematical Physics:** Linear vector space, matrices; vector calculus; linear differential
equations; elements of complex analysis; Laplace transforms, Fourier
analysis, elementary ideas about tensors.

**Classical Mechanics: **Conservation laws;
central forces; collisions and scattering in laboratory and centre of
mass reference frames; mechanics of system of particles; rigid body
dynamics; moment of inertia tensor; noninertial frames and pseudo forces; variational principle;
Lagrange’s and Hamilton’s formalisms; equation of motion, cyclic
coordinates, Poisson bracket; periodic motion, small oscillations,
normal modes; wave equation and wave propagation; special theory of relativity – Lorentz transformations, relativistic kinematics, mass-energy equivalence.

**Electromagnetic Theory:** Laplace and Poisson
equations; conductors and dielectrics; boundary value problems;
Ampere’s and Biot-Savart’s laws; Faraday’s law; Maxwell’s equations;
scalar and vector potentials; Coulomb and Lorentz gauges; boundary
conditions at interfaces; electromagnetic waves; interference,
diffraction and polarization; radiation from moving charges.

**Quantum Mechanics:** Physical basis of quantum
mechanics; uncertainty principle; Schrodinger equation; one and three
dimensional potential problems; Particle in a box, harmonic oscillator,
hydrogen atom; linear vectors and operators in Hilbert space; angular
momentum and spin; addition of angular momentum; time independent
perturbation theory; elementary scattering theory.

**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;
X-ray spectra; rotational and vibrational spectra of diatomic
molecules; electronic transition in diatomic molecules, Franck-Condon
principle; Raman effect; NMR and ESR; lasers.

**Thermodynamics and Statistical Physics:** Laws of
thermodynamics; macrostates, phase space; probability 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, critical point.

**Solid State Physics: **Elements of crystallography; diffraction methods for structure determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors and insulators; transport properties; optical, dielectric and magnetic properties of solids; elements of superconductivity.

**Nuclear and Particle Physics:** Rutheford scattering; basic properties of nuclei; radioactive decay; nuclear forces; two nucleon problem; nuclear reactions; conservation laws;
fission and fusion; nuclear models; particle accelerators, detectors;
elementary particles; photons, baryons, mesons and leptons; Quark model.

**Electronics:** Network analysis; semiconductor devices; bipolar transistors; FETs; power supplies, amplifier, oscillators; operational amplifiers; elements of digital electronics; logic circuits.