Physics (PH)

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
• Addition of angular momenta
• 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.