Syllabus for the written test (DST funded JRF position in Atomic and Molecular Physics) 1) Electrodynamics and Special Relativity: 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, energy level 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, laser 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 temperatures 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, photoelectric effect 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. .