GATE Physics Syllabus

Subject Code: PH

Course Structure

Course Syllabus

Section 1: Mathematical Physics

• Linear vector space −
  • Basis
  • Orthogonality
  • Completeness
• Matrices
• Vector calculus
• Linear differential equations, elements of complex analysis
• Cauchy Riemann conditions −
  • Cauchy’s theorems
  • Singularities
  • Residue theorem
  • Applications
• Laplace transforms −
  • Fourier analysis
• Elementary ideas about tensors −
  • Covariant and contravariant tensor
  • Levi-Civita and Christoffel symbols

Section 2: Classical Mechanics

• D’Alembert’s principle
• Cyclic coordinates
• Variational principle
• Lagrange’s equation of motion
• central force and scattering problems
• Rigid body motion
• Small oscillations
• Hamilton’s formalisms
• Poisson bracket
• special theory of relativity −
  • Lorentz transformations
  • Relativistic kinematics
  • Mass-energy equivalence

Section 3: Electromagnetic Theory

• Solutions of electrostatic and magnetostatic problems including boundary value

• Problems

• Dielectrics and conductors

• Maxwell’s equations

• Scalar and vector potentials

• Coulomb and Lorentz gauges

• Electromagnetic waves and their reflection, refraction, interference, diffraction and polarization

• Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves

• Radiation from a moving charge

Section 4: Quantum Mechanics

• Postulates of quantum mechanics

• Uncertainty principle

• Schrodinger equation

• One-, two- and three-dimensional potential problems

• Particle in a box, transmission through one dimensional potential barriers, harmonic oscillator, hydrogen atom

• Linear vectors and operators in Hilbert space

• Angular momentum and spin

• Addition of angular momenta

• Time independent perturbation theory

• Elementary scattering theory

Section 5: 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

Section 6: 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
• Rotational and vibrational spectra of diatomic molecules
• Electronic transition in diatomic molecules, Franck-Condon principle
• Raman effect
• NMR, ESR, X-Ray Spectra
• Lasers −
  • Einstein coefficients
  • Population inversion
  • Two and three level systems

Section 7: Solid State Physics & Electronics

• Elements of crystallography

• Diffraction methods for structure determination

• Bonding in solids

• Lattice vibrations and thermal properties of solids

• Free electron theory

• Band theory of solids −

  • Nearly free electron and tight binding models

• Metals, semiconductors and insulators

• Conductivity, mobility and effective mass

• Optical, dielectric and magnetic properties of solids

• Elements of superconductivity −

  • Type-I and Type II superconductors

  • Meissner effect

  • London equation

• Semiconductor devices −

  • Diodes

  • Bipolar junction transistors

  • Field effect transistors

• Operational amplifiers −

  • Negative feedback circuits

  • Active filters and oscillators

• Regulated power supplies

• Basic digital logic circuits, sequential circuits, flip-flops, counters, registers, A/D and D/A conversion

Section 8: Nuclear and Particle Physics

• Nuclear radii and charge distributions, nuclear binding energy, electric and Magnetic moments
• Nuclear models, liquid drop model −
  • Semi-empirical mass formula
  • Fermi gas model of nucleus
  • Nuclear shell model
• Nuclear force and two nucleon problem
• Alpha decay, beta-decay, electromagnetic transitions in nuclei
• Rutherford scattering, nuclear reactions, conservation laws
• Fission and fusion
• Particle accelerators and detectors
• Elementary particles, photons, baryons, mesons and leptons
• Quark model

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