## Joint Entrance Screening Test

### Syllabus

Mathematical Methods

Vector algebra and vector calculus, tensors, curvilinear coordinate systems, linear algebra; Linear differential equations, elements of Sturm–Liouville theory; Special functions; Complex analysis; Fourier series and Fourier transforms, Laplace transforms; Elementary properties of discrete groups; Elements of probability theory, error analysis.

Classical Mechanics

Newton’s laws, conservation of energy and momentum, collisions; generalized coordinates, principle of least action, Lagrangian and Hamiltonian formulations of mechanics; Symmetry and conservation laws; central force problem, Kepler problem; Small oscillations and normal modes; special relativity in classical mechanics.

Electromagnetism & Optics

Electrostatics and magnetostatics, boundary value problems, multipole expansion;

Fields in conducting, dielectric, diamagnetic, and paramagnetic media; Faraday’s law and time-varying fields; displacement current; Maxwell’s equations; energy and momentum of electromagnetic fields; Propagation of plane electromagnetic waves, reflection, refraction; Electromagnetic waves in dispersive and conducting media; diffraction, interference, polarization.

Quantum Mechanics

Uncertainty principle; Schrodinger equation; central potentials, hydrogen atom; Orbital and spin angular momenta, the addition of angular momenta; Matrix formulation of quantum theory, unitary transformations, Hermitian operators; Variational principle, time-independent perturbation theory, time-dependent perturbation theory.

Thermodynamics & Statistical Physics

Laws of thermodynamics, work, and heat, thermodynamic potentials; Elements of kinetic theory; Maxwell’s relations; Statistical ensembles; partition function; classical ideal gas, harmonic oscillators; Classical and quantum statistics; Fermi and Bose gases; black body radiation; statistics of paramagnetism

Electronics

Basics of semiconductor; p-n junctions, diodes, transistors; LCR circuits, rectifiers, amplifiers, active filters, and oscillators; basics of OPAMPs and their applications; basics of digital electronics.

Applicants seeking admission for a Ph.D. / Integrated Ph.D. Programme in Physics or Theoretical Computer Science or Neuroscience or Computational Biology in one of the Participating Institutes may appear for the Joint Entrance Screening Test (JEST).

The Science & Engineering Research Board (SERB) (statutory body established through an Act of Parliament) recognizes JEST as a National Eligibility Test (NET). Fellows working in SERB programmes and qualified in NET are eligible to get the enhanced fellowship.

Participating Institutes have their own eligibility criteria. Applicants who are expected to complete their final examinations by August of each year are also eligible to appear for the JEST exam of that year.