Syllabus for the written test (DST funded JRF position in Atomic and Molecular ) 1) Electrodynamics and : Electromagnetic Waves: Waves in one-dimension – Wave eqaution – sinusoidal waves – Reflection and transmission – Polarization – Electromagnetic waves in vacuum – wave equations for E and B – Monochromatic plane waves – Energy and momentum in electromagnetic waves – Electromagnetic Waves in Matter – Propagation in linear media – reflection and transmission at normal and oblique incidence – Absorption and Dispersion – Electromagnetic waves in conductors – reflection at a conducting surface – frequency dependence of permittivity – Guided Waves – wave guides – TE waves in a rectangular wave guide – waves in coaxial transmission line. Potentials and Fields: Scalar and vector potentials, guage transformations – Coulumb gauge. Radiation: Dipole radiation – Electric and magnetic dipole radiation, radiation from an arbitrary source, Power radiated from point charges, Radiation reaction. Electrodynamics and Relativity: Special theory – Einstein's postulates – Geometry and structure of spacetime – Lorentz transformations. Relativistic mechanics – Propertime – Energy and Momentum – Kinematics and Dynamics; Relativitistic electrodynamics – Magnetism as a relativistic phenomenon – field tensor – transformation of fields – Relativistic potentials

2) Quantum Mechanics: Mathematical Introduction: Linear vector spaces, inner products, linear operators, eigenvalue problem, generalization to infinite dimensions. Towards quantum mechanics: relevant experiments, wave particle duality, uncertainty principle, postulates of quantum mechanics, Schrodinger equation, probability current and conservation. Simple one-dimensional potential problems: Free particle, particle in a box; scattering in step-potentials, transmission and reflection coefficients. Harmonic oscillator: Obtaining eigenvalues and eigenfunctions using ladder operators. Angular momentum: Rotations in three dimensions, eigenvalue problem of L2 and Lz. Hydrogen atom: Eigenvalue problem, degeneracy of the spectrum, numerical estimates and comparison with 30 experiments Approximation methods: Variational methods, WKB approximation; time-indepdndent perturbation theory; time-dependent perturbation theory: Interaction picture, Fermi's golden rule, sudden and adiabatic approximations. Symmetries in quantum mechanics: Continuous symmetries: space and time translations, rotations; rotation group and its irreducible representations; Irreducible spherical tensor operators, Wigner-Eckart theorem. Discrete symetries: parity and time reversal. Identical particles: Meaning of identity and consequences; symmetric and antisymmetric wavefunctions; Slater determinant.

3) Atomic and molecular physics: Atomic structure and spectroscopy: One and multi electron atoms, notation schemes, interaction of electromagnetic radiation with atoms, Einstein’s coefficients, line shape and broadening. Visible, UV and x-ray spectroscopy of atoms. Instrumentation and applications. Astronomical significance. Molecular spectroscopy: Molecular structure, Group theory for molecular physics, Huckel model, Hartree Fock, density functional calculation of di-atomic and poly-atomic molecules. Energy level structure and notation, electronics, vibrational and rotational structure. Visible, IR and microwave spectroscopy. Raman spectroscopy and its applications. Resonance spectroscopy: Electron spin resonance, nuclear magnetic resonance, Mganetic Resonance Imaging. Mossbauer spectroscopy. Mass spectroscopy: Mass spectrometer basics, instrumentation, ion traps as mass spectrometers, Paul and Penning traps, multipole traps. Fourier transform infrared spectroscopy. Cold atoms: Cooling of atoms, techniques, cooling, magneto optical traps, BEC, spectroscopy in condensates, frequency standards.

4) Experimental physics: Essential techniques: Probability distributions and statiscs, error analysis and error propagation, covariance, least-square fitting. Vacuum technology: gas flow equations, flow regimes, types of pumps, gauges and seals. Sensors and analog instrumentation: analog signal processing. Lock in amplifiers and applications: measurements in noise prone environments. Digital electronics: microprocessors and micro-controllers, ADC/DAC, PLCs, computer interfaces. Virtual instrumetation: General purpose instrumentation and interface, virtual instrumentation techniques and programming. Fundamental methods in experimental physics: Coincidence techniques in time correlated measurements. Null measurements. Spectroscopy: Spectrophotometers, Laser Raman spectroscopy, Resonance spectroscopy, NMR, ESR, Mossbauer spectroscopy. Mass spectrometry and applications. Cryogenics: production, measurement, low and ultra-low using liquid nitrogen. He cryostats, adiabatic and nuclear de-magnetization, dilution refrigerators.

5) Statistical Mechanics Introduction to statistical physics: statistical description of system of particles, microstates, ensembles, microcanonical ensembles, canonical ensembles, partition functions, free energy, chemical potential, grand canonical ensembles. Maxwell-Boltzmann velocity and speed distributions, thermodynamics of blackbody radiation. Specific heat of solids and lattice vibrations: Breakdown of classical theory, Einstein’s theory of specific heat, Debye approximation. Elementary excitations in liquid helium II. Free electron theory of metals: The electronic specific heat, thermionic emission from metals, of metals. Statistical equilibrium of white dwarf stars. Statistical model of the atom. Electron distribution in insulators and semiconductors. Phase transitions: Critical exponents, Ising model, mean field theory. Statistical mechanics of interacting systems: the method of quantized fields.