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The Joint Entrance Screening Test (JEST) is a national level qualifying examination for admissions to PhD programmes in Physics at premier Indian research institutions and a PhD programme in Theoretical Computer Science at the Institute of Mathematical Sciences.

Using JEST results, each institute will call a limited number of candidates for its own selection procedure depending, on its requirements. All selected candidates will receive Research Fellowships from the respective institutes.

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## Joint Entrance Screening Test (JEST) Syllabus

### Physics Syllabus

#### Mathematical Methods

Vector algebra and vector calculus; linear vector spaces, linear operators, matrices and Eigenvalue problem; SturmLiouville theory, classical orthogonal polynomials; linear ordinary differential equations, exact and series methods of solution ; linear partial differential equations, solution by separation of variables; complex variables, analytic functions, Taylor and Laurent expansions, contour integration; Fourier and Laplace transforms.

#### Classical Mechanics

Newton's laws, conservation of energy and momentum, collisions; generalized coordinates, the principle of least action, Lagrangian and Hamiltonian formulations of mechanics; symmetry and conservation laws; central force problem, Kepler problem; rigid body motion; small oscillations and normal modes; special relativity in classical mechanics.

#### Electromagnetic Theory

Laws of electrostatics and magnetostatics, methods of solving boundary value problems, multipole expansion; fields in conducting, dielectric, diamagnetic and paramagnetic materials; Faradays law and time varying fields; conservation of charge, displacement current; Maxwells equations; energy and momentum of electromagnetic fields, Poynting theorem; propagation of plane electromagnetic waves, reflection and refraction of plane electromagnetic waves, electromagnetic waves in dispersive and conducting media; scalar and vector potentials, Coulomb and Lorentz gauge, wave equation in terms of electromagnetic potentials; radiation from moving charges, retarded and advanced potentials,

Lienard-Wiechert potentials, multipole radiation, Larmor formula.

#### Quantum Mechanics

The uncertainty principle; conceptual basis of quantum mechanics; Schrodinger equation, problems in one, two and three dimensions, bound states and tunnelling, particle in a box, harmonic oscillator, hydrogen atom; matrix formulation of quantum theory, unitary transformations and Hermitian operators and their properties; orbital and spin angular momenta, addition of angular momenta; time independent and time dependent perturbation theory, Fermi golden rule; elementary scattering theory.

#### Thermodynamics and Statistical Physics

Laws of thermodynamics; work and heat; thermodynamic potentials, Maxwell's relations; statistical ensembles; partition function; classical ideal gas, harmonic oscillators; classical and quantum statistics; Fermi and Bose gases; black body radiation; first and second order phase transitions.

#### Solid State Physics

Simple crystal structures and X-ray diffraction; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors, and insulators; basic electrical, optical and magnetic properties of solids; elements of superconductivity.

Electronics Diodes, rectifier circuits, junctions, transistors and field effect devices; device characteristics, frequency dependence and applications like active filters and oscillator circuits; solar cells, photodetectors, and LEDs; operational amplifiers and their applications; Boolean algebra, digital techniques and applications: registers, counters, comparators and similar circuits; A/D and D/A converters; microprocessor and microcontroller basics.

#### Nuclear and Particle Physics

The structure of the nucleus; binding energy, nuclear fusion and fission; radioactive decay, barrier penetration by alpha particles; classification of elementary particles and fundamental interactions, leptons and hadrons, elementary ideas of quark model; conservation laws in particle reactions.

#### Atomic and Optical Physics

Interference, diffraction, and polarization of light; photoelectric effect; spectra of single and multiple electron atoms; Zeeman and Stark effects; electric dipole transition and selection rules; hyperfine structure; spontaneous and stimulated emission.

#### Experimental data and error analysis Probability theory

Gaussian and Poisson distributions; error analysis; propagation of errors; significant figures; least square fitting

### Mathematics

Mathematic syllabus will cover all books units of B.Sc maths and most of the portion of exam will from the books of M.Sc.

### JEST (Theoretical Computer Science)

- Elements of Discrete Mathematics
- Discrete Mathematical Structures with Applications to Computer Science,
- Compilers: Principles, Techniques and Tools
- Fundamentals of Data Structures
- An Introduction to Data Structures with Applications
- Fundamentals of Computer Algorithms
- The Design and Analysis of Computer Algorithms
- Introduction to Algorithms