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# Syllabus For CSIR-UGC NET National Eligibility Test rpsc.rajasthan.gov.in : Public Service Commission

** Organisation **: Rajastan Public Service Commission

**: Syllabus**

__Announcement__**: CSIR-UGC National Eligibility Test (NET)**

__Name of Examination__**: Junior Research Fellowship and Lecturership**

__Applicable For__** Download Syllabus **: http://www.syllabus.gen.in/uploads/545-CSIR.pdf

**: https://rpsc.rajasthan.gov.in/**

__Home Page__## CSIR-UGC NET Syllabus :

** Physical Sciences **:

**Part ‘A’ Core**

**:**

__I.____Mathematical Methods of Physics__Dimensional analysis. Vector algebra and vector calculus. Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigen vectors.Linear ordinary differential equations of first & second order, Special functions (Hermite, Bessel, Laguerre and Legendre functions).

Related: Rajasthan Public Service Commission Syllabus for Assistant Prosecution Officer : www.syllabus.gen.in/430.html

Fourier series, Fourier and Laplace transforms. Elements of complex analysis, analytic functions; Taylor & Laurent series; poles, residues and evaluation of integrals. Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem.

** II.Classical Mechanics **:

Newton’s laws. Dynamical systems, Phase space dynamics, stability analysis. Central force motions. Two body Collisions -scatterin g in laboratory and Centre of mass frames. Rigid body dynamics-moment of inertia tensor. Non-inertial frames and pseudo forces.

Variational principle. Generalized coordinates. Lagrangian and Hamiltonian formalism and equations of motion. Conservation laws and cyclic coordinates. Periodic motion: small oscillations, normal modes. Special theory of relativity-Lorentz transformations, relativistic kinematics and mass–energy equivalence.

** III.Electromagnetic Theory **:

**: Gauss’s law and its applications, Laplace and Poisson equations, boundary value problems.Magneto statics: Biot-Savart law, Ampere’s theorem. Electromagnetic induction. Maxwell’s equations in free space and linear isotropic media; boundary conditions on the fields at interfaces.**

__Electrostatics__Scalar and vector potentials, gauge invariance. Electromagnetic waves in free space. Dielectrics and conductors. Reflection and refraction, polarization, Fresnel’s law, interference, coherence, and diffraction. Dynamics of charged particles in static and uniform electromagnetic fields.

** IV.Quantum Mechanics **:

Wave-particle duality. Schrödinger equation (time-dependent and time-independent). Eigenvalue problems (particle in a box, harmonic oscillator, etc.). Tunneling through a barrier. Wave-function in coordinate and momentum representations. Commutators and Heisenberg uncertainty principle.

Dirac notation for state vectors. Motion in a central potential: orbital angular momentum, angular momentum algebra, spin, addition of angular momenta; Hydrogen atom. Stern-Gerlach experiment. Time-independent perturbation theory and applications.Variational method. Time dependent perturbation theory and Fermi’s golden rule, selection rules. Identical particles, Pauli exclusion principle, spin-statistics connection.

** V.Thermodynamic and Statistical Physics **:

Laws of thermodynamics and their consequences. Thermodynamic potentials, Maxwell relations, chemical potential, phase equilibrium. Phase space, micro-and macro-states. Micro-canonical, canonical and grand-canonical ensembles and partition functions. Free energy and its connection with thermodynamic quantities. Classical and quantum statistics. Ideal Bose and Fermi gases. Principle of detailed balance. Black body radiation and Planck’s distribution Law.

** Part ‘B’ Advanced **:

**:**

__I.Mathematical Methods of Physics__Green’s function. Partial differential equations (Laplace, wave and heat equations in two and three dimensions). Elements of computational techniques: root of functions, interpolation, extrapolation, integration by trapezoid and Simpson’s rule, Solution of first order differential equation using Runge-Kutta method. Finite difference methods. Tensors. Introductory group theory: SU(2), O(3).

** II. Classical Mechanics **:

Dynamical systems, Phase space dynamics, stability analysis.Poisson brackets and canonical transformations. Symmetry, invariance and Noether’s theorem. Hamilton-Jacobi theory.

__ III.Electromagnetic Theory__ :

Dispersion relations in plasma. Lorentz invariance of Maxwell’s equation. Transmission lines and wave guides. Radiation-from moving charges and dipoles and retarded potentials.

** IV.Quantum Mechanics :**

Spin-orbit coupling, fine structure. WKB approximation. Elementary theory of scattering : phase shifts, partial waves, Born approximation. Relativistic quantum mechanics: Klein-Gordon and Dirac equations. Semi-classical theory of radiation.