# Physics (PH)

Are you preparing for the GATE 2022 examination with Physics as your subject? Find out the complete Physics syllabus in detail here!

Candidates taking the Graduate Aptitude Test in Engineering (GATE) 2022 Examination with Physics (Code: PH) as a subject must go through the entire syllabus. The Physics syllabus is divided into 9 subjects with various topics under each section:

## Section 1: Mathematical Physics

• Vector calculus:
• Elementary ideas about tensors: covariant and contravariant tensors
• Linear differential equations: second order linear differential equations and solutions involving special functions
• Linear vector space: basis, orthogonality and completeness, matrices, similarity transformations, diagonalization, eigenvalues and eigenvectors
•  Complex analysis:Cauchy-Riemann conditions, Cauchy’s theorem, singularities, residue theorem and applications, Laplace transform, Fourier analysis

## Section 2: Classical Mechanics

• Lagrangian formulation:
• Euler-Lagrange equation
• D’Alembert’s principle
• Calculus of variations
• Central force motion: Kepler problem and Rutherford scattering
• Hamilton’s principle
• Symmetry and conservation laws
• Rigid body dynamics: inertia tensor, orthogonal transformations, Euler angles, Torque free motion of a symmetric top
• Liouville’s theorem
• Small oscillations: coupled oscillations and normal modes
• Hamiltonian and Hamilton’s equations of motion
• Canonical transformations: action-angle variables, Poisson brackets, Hamilton-Jacobi equation
• Special theory of relativity:
• Relativistic kinematics
• Lorentz transformations
• Mass-energy equivalence

## Section 3: Electromagnetic Theory

• Method of images
• Solutions of electrostatic and magnetostatic problems including boundary value problems
• Separation of variables
• Magnetic materials
• Dielectrics and conductors
• Scalar and vector potentials
• Electromagnetic waves in free space, non-conducting and conducting media
• Reflection and transmission at normal and oblique incidences
• Radiation from a moving charge
• Multipole expansion
• Maxwell’s equations
• Coulomb and Lorentz gauges
• Polarization of electromagnetic waves
• Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves

## Section 4: Quantum Mechanics

• Uncertainty principle
• Postulates of quantum mechanics
• Schrodinger equation
• Hydrogen atom
• One dimensional potentials: step potential, finite rectangular well, tunneling from a potential barrier, particle in a box, harmonic oscillator
• Dirac Bra-Ket notation, linear vectors and operators in Hilbert space
• Two and three dimensional systems: concept of degeneracy
• Angular momentum and spin
• Elementary scattering theory, Born approximation
• Symmetries in quantum mechanical systems
• Variational method and WKB approximation, time independent perturbation theory

## Section 5: Thermodynamics and Statistical Physics

• Laws of thermodynamics
• Phase space ensembles
• Macrostates and microstates
• Partition function, free energy, calculation of thermodynamic quantities
• Degenerate Fermi gas
• Classical and quantum statistics
• Black body radiation and Planck’s distribution law
• First and second order phase transitions
• Phase equilibria
• Bose-Einstein condensation
• Critical point

## Section 6: Atomic and Molecular Physics

• Spectra of one-and many-electron atoms
• Fine and hyperfine structures
• Spin-orbit interaction: LS and jj couplings
• Zeeman and Stark effects
• Rotational and vibrational spectra of diatomic molecules
• Electric dipole transitions and selection rules
• Electronic transitions in diatomic molecules, Franck-Condon principle
• EPR, NMR, ESR, X-ray spectra
• Raman effect
• Lasers: Einstein coefficients, Population inversion, Two and three level systems

## Section 7: Solid State Physics

• Elements of crystallography
• Bonding in solids
• Diffraction methods for structure determination
• Lattice vibrations and thermal properties of solids
• Free electron theory
• Conductivity, mobility and effective mass
• Band theory of solids: nearly free electron and tight binding models metals, semiconductors and insulators
• Optical properties of solids
• Dielectric properties of solid
• Kramer’s-Kronig relation, intra- and inter-band transitions
• Dielectric function, polarizability, ferroelectricity
• Dia, para, ferro, antiferro and ferri-magnetism, domains and magnetic anisotropy
• Magnetic properties of solids
• Superconductivity: Type-I and Type II superconductors, Meissner effect, London equation, BCS Theory, Flux quantization

## Section 8: Electronics

• Semiconductors in equilibrium:
• Electron and hole statistics in intrinsic and extrinsic semiconductors
• Metal-semiconductor junctions
• PN diodes, bipolar junction transistors, field effect transistors
• Ohmic and rectifying contacts
• Negative and positive feedback circuits
• Oscillators, operational amplifiers, active filters
• Basics of digital logic circuits
• Combinational and sequential circuits
• Flipflops
• Timers
• Counters
• Registers
• A/D and D/A conversion

## Section 9: Nuclear and Particle Physics

• Semi empirical mass formula
• Nuclear radii and charge distributions, nuclear binding energy, electric and magnetic moments
• Nuclear models
• Nuclear force and two nucleon problem
• Liquid drop model, nuclear shell model
• Alpha decay, beta-decay, electromagnetic transitions in nuclei
• Fission and fusion
• Rutherford scattering, nuclear reactions, conservation laws
• Particle accelerators and detectors
• Elementary particles
• Quark model
• Photons, baryons, mesons and leptons
• Conservation laws, isospin symmetry, charge conjugation, parity and time-reversal invariance.