One of the most difficult government examinations in India is the CSIR Physical Sciences test. One of the five science and technology fields that demand extensive study from students in order to successfully complete the exam is physical science. The NET exam is where most students who want to pursue physics as a career in the future start. It undoubtedly offers a significant chance to realise the desire of becoming a physicist.
1) Mathematical Methods of Physics
Dimensional analysis
Vector algebra and vector calculus.
Linear algebra
Matrices Cayley-Hamilton Theorem
Eigenvalues and eigenvectors
Linear ordinary differential equations of first & second order
Special functions (Hermite, Bessel, Laguerre and Legendre functions)
Fourier series, Fourier and Laplace transforms
Elements of complex analysis, analytic functions
Taylor & Laurent series; residues, poles and evaluation of integrals.
Elementary probability theory, random variables, binomial
Poisson and normal distributions.
Central limit theorem.
2) Classical Mechanics
Newton’s laws
Dynamical systems
Phase space dynamics, stability analysis.
Central force motions.
Two body Collisions – scattering 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
3) Electromagnetic Theory
Electrostatics: Gauss’s law and its applications
Laplace and Poisson equations, boundary value problems.
Magnetostatics: 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.
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.
4.Quantum Mechanics
Wave-particle duality.
Schrödinger equation (time-dependent and time-independent).
Eigenvalue problems (harmonic oscillator, particle in a box, 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.
5) Thermodynamic and Statistical Physics
Laws of thermodynamics and their consequences.
Thermodynamic potentials
Maxwell relations, chemical potential, phase equilibria.
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.
Blackbody radiation and Planck’s distribution law.
6) Electronics and Experimental Methods
Semiconductor devices (transistors, diodes, junctions, field effect devices, homo- and hetero-junction devices), device characteristics, device structure, frequency dependence and applications.
Opto-electronic devices (solar cells, photo-detectors, LEDs).
Operational amplifiers and their applications.
Digital techniques and applications (counters, registers, comparators and similar circuits).
A/D and D/A converters.
Microprocessor and microcontroller basics.
Data interpretation and analysis.
Precision and accuracy.
Error analysis, propagation of errors.
Least Squares fitting,
