Physics [PH 101]

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Credit
L | T | P | C
3 | 2 | 0 | 4

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Introduction of vector analysis and calculus. Grad, div and curl. Line, surface and volume integrals. Gauss and Stokes’ theorem. Curvilinear coordinate system, Dirac delta function. Concept of electric and magnetic fields. Electrostatic potential, Poisson and Laplace’s equation. Multipole expansion. Biot-Savart Law, Ampere and Faraday’s law. Electromagnetic induction. Conservation equation, introduction to Maxwell’s equations. Electromagnetic waves, Waveguides. Stern Gerlach experiment. Limitations of classical concepts. Kets, bras, and operators, Hilbert space, postulates of quantum mechanics, measurements and observables, expectation value, Ehrenfest theorems. Schrodinger equation, position and momentum representation. Wave-function, particle in a box, potential well, tunneling and it’s applications, periodic potential. Electron band structure in solids.

Physics Laboratory [PH 102]

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Credit
L | T | P | C
0 | 0 | 4 | 2

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Error analysis; Probability and Statistics; Compound pendulum; Newton’s Rings; Diffraction grating; Fresnel’s biprism; e/m by Thomson’s method; Planck’s constant; Frank Hertz experiment; Helmholtz coil; B-H Curve tracer; Dielectric constant of solids; Moving coil galvanometer; Thermistor characteristics; Lissajous figures; Stefan’s constant

Molecular and Crystal Physics [PH 404]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Introduction: an overview of fundamental of crystallography and the module introduces to the geometry of crystalline state, scattering of x-rays,Diffraction from a crystal and experimental methods to collect diffraction data and analyze. Symmetry in crystal lattice, Chemical bonds, Diffraction from periodic structures and methods of structure solving and solutions.

Crystal growth and crystal defects - It deals with the theory and kinetics of crystal growth, the various techniques such as melt growth, solution growth, vapour growth and the study of defects and crystals.

Lab Experimental demonstration: Powder X-ray diffraction analysis of solids in polycrystalline form and to find out the crystal systems by indexing the data sets.

Introduction to the Special Theory of Relativity [PH 406]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Overview of Newtonian Mechanics: Galilean Relativity, Incompatibility with Electromagnetism, Michelson-Morley Experiment and the Aether Hypothesis. Postulates of Special Relativity: Lorentz transformations, Relativity of Simultaneity, Time dilation and Length contraction, Doppler Effect; Understanding Relativity through paradoxes: Pole and Barn Paradox, Twin Paradox.

Mathematics of Special Relativity: Notion of four-vectors; Covariant and contravariant four-vectors; notion of invariant distance; four-vector calculus; Tensors and their transformation properties; Tensor calculus; Causality and the Causal structure of space-time, space-time diagrams.

Relativistic Dynamics: Mass-energy equivalence; Relativistic treatment of collisions and decays; Relativistic electrodynamics and covariant formulation of Maxwell equations.

Experimental verifications of Special Relativity: Kennedy-Thorndike experiment, Ives-Stilwell experiment. High energy collision of elementary particles (LHC, LEP) and fundamental tests of Special Relativity.

Introduction to Lagrangian Mechanics [PH 407]

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Credit
L | T | P | C
3 | 0 | 0 | 2

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Review of Newtonian mechanics for a single and many particles, Constraints, Holonomic and Nonholonomic constraints, Generalized coordinates, Lagrange multipliers, Principle of virtual work; D'Alembert principle, Euler-Lagrange’s equation, Velocity-dependent potentials and the dissipation functions, Hamilton’s principle, Calculus of variation, Lagrange’s equation from Hamilton’s principle, Cyclic coordinates, Conservation theorems and symmetry principles, Noether’s theorem.

Application of Lagrangian Mechanics: Central forces, Kepler’s problem, Laplace-Runge-Lenz vector.

Waves and Oscillations [PH 408]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Periodic Motions: Simple harmonic oscillator (SHO), Superposition of vibrations: Lissajous Figures, Parallel and perpendicular superposition, examples of free vibrations in physical system: mass-spring system, Young Modulus, Pendulum etc.

Forced Vibrations: Undammed oscillator with force term, Forced oscillation with damping, Transient phenomena, Examples of resonance: Electrical, optical, nuclear resonance, Anharmonic oscillator.

Coupled Oscillators: Introduction of the concept of normal modes, natural frequency, forced vibrations and resonance of two coupled oscillator, generalization of N coupled oscillator: finding normal modes for N coupled oscillator, Longitudinal oscillations, normal modes for crystal lattice, stretched string, Longitudinal vibrations of a rod, vibrations of air columns, elasticity of gas, normal modes of two and three dimensional systems, Fourier analysis of normal modes problem, quasi normal modes and dissipation.

Progressive Waves: Travelling waves, progressive waves in specific media, superposition of wave pulses, Dispersion; phase and group velocities, transport of energy by the wave, momentum flow and mechanical radiation pressure, Polarization, solutions of the wave equation in even and odd dimensions.

Interference: The Huygens-Fresnel Principle, Reflection and refraction of plane waves, Doppler effect, Double slit interference, Diffraction by single slit, Diffraction grating, Fraunhofer vs Fresnel diffraction.

Mathematical Methods of Physics - I [PH 502]

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Credit
L | T | P | C
3 | 1 | 0 | 4

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Finite and infinite dimensional vector spaces, Hilbert space, operators in infinite dimensional spaces, Matrix algebra, Cayley-Hamilton theorem; Gram-Schmidt orthogonalization, commuting matrices with degenerate eigenvalues.

Algebra of complex numbers, Schwarz inequality, function of a complex variable, Cauchy- Riemann equations and their applications, harmonic functions, complex integrals, Cauchy's theorem and its corollaries, Taylor and Laurent expansion, classification of singularities, branch point and branch cut, residue theorem and evaluation of integrals.

Theory of second order linear homogeneous differential equations, Frobenius method, Fuch's theorem, Sturm- Liouville theory, Hermitian operators, orthogonal expansion and completeness. Inhomogeneous differential equations, Green's functions, special functions (Bessel, Legendre, Hermite and Laguerre functions) and properties.

Integral transforms: Fourier and Laplace transforms and their inverse transforms, solution of differential equations using integral transform.

Elementary group theory, point symmetry groups, group representations reducible and irreducible representations, Lie groups and Lie algebra with SU(2) as an example.

Quantum Mechanics I [PH 503]

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Credit
L | T | P | C
3 | 1 | 0 | 4

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Wave functions, superposition principle, wave packets, Schrodinger equation, probability and current densities, expectation values and Ehrenfest"s theorem.

Linear vectors and operators in Hillbert space, observables, commuting operators, momentum representation and uncertainty principle, unitary transformations, Schrodinger and Heisenberg representations, equations of motion.

Applications: one-dimensional potential problems, linear harmonic oscillator with polynomial solutions, and creation and annihilation operators.

Central forces, free and bound states in a Coulomb potential, angular momentum, spherical harmonics, Stern- Gerlach experiment for spin ½ system, spin, addition of angular momenta, Clebsch-Gordan coefficients. Time independent perturbation theory, first and second order corrections to the energy eigenvalues, degenerate perturbation theory, application to one-electron system, Zeeman effect and Stark effect. Variational methods: Helium atom as example, Ritz principle for excited states.

Special topics like Quantum dots, coherent and squeezed states, lasers, Aharonov-Bohm effect, Berry phases, quantum entanglement and EPR paradox.

Quantum Mechanics II [PH 504]

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Credit
L | T | P | C
3 | 1 | 0 | 4

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Time dependent perturbation theory, interaction picture, Fermi’s Golden rule, sudden and adiabatic approximations. WKB approximation, tunneling through a barrier.

Scattering theory, differential and total scattering cross-sections, Scattering by spherically symmetric potentials, Partial wave analysis and phase shifts, Coulomb scattering, Green’s function in scattering theory, Born approximation.

Symmetries in quantum mechanics, Conservation laws and symmetries: continuous and discrete, Rotation group, SO(3) and SU(2) representation, Lorentz group, SL(2,C) representation, matrix representation of generators , Irreducible spherical tensor operators, parity and time reversal. Identical Particles, symmetric and antisymmetric wavefunctions, slater determinant, Symmetric and antisymmetric spin wavefunctions of two identical particles, algebra of bosonic and fermionic creation an annihilation operators, continuous one particle spectrum and quantum field operators, dynamics of identical particles.

Relativistic quantum mechanics, Klein-Gordon equation, negative energy states and concept of antiparticles, Dirac equation, plane wave solution and momentum space spinors, Helicity and chirality, charge conjugation.

Special Topics: Many body physics, Gross-Pitaevskii equation, Bose-Einstein Condenstation, Superfluidty, Quantum well lasers, Nuclear magnetic resonance, Electron Spin resonance, Raman Effect, fractional braiding statistics in quantum Hall systems, qubits and quantum computing.

Classical Electrodynamics [PH 505]

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Credit
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3 | 1 | 0 | 4

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Review of electrostatics and magnetostatics: Laplace and Poisson equations, uniqueness theorem, boundary- value problems, Lorentz force.

Maxwell’s equations, electromagnetic waves, Poynting theorem. Gauge transformations and gauge invariance, electromagnetic potentials, wave propagation in conductors and dielectrics, Lorentz theory of dispersion, complex refractive index.

Special relativity, Minkowski space and four vectors, concept of four-velocity, four acceleration and higher rank tensors, relativistic formulation of electrodynamics, Maxwell equations in covariant form, gauge invariance and four-potential, the action principle and electromagnetic energy momentum tensor.

Liénard-Weichert potentials, radiation from an accelerated charge, Larmor formula, Bremsstrahlung and synchrotron radiation, multipole radiation, dispersion theory, radiative reaction, radiative damping, scattering by free charges; applications to wave-guides, fibres and plasmas.

Radiation reaction from energy conservation; Problem with Abraham-Lorentz formula; Limitations of Classical electrodynamics.

Special Lecture Topics: Plasma physics , Plasma and its occurrence in nature, uniform but time-dependent magnetic field : Magnetic pumping; Magnetic bottle and loss cone; MHD equations, Magnetic Reynold's number, Pinched plasma; Bennett's relation.

Methods of Experimental Physics [PH 506]

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Credit
L | T | P | C
1 | 0 | 4 | 4

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Data visualization, elements of data analysis, linear and non-linear regression. General Physics and Optics: determination of Hall effect coefficient in n and p-type semiconductors, determination of electrical resistivity of a semiconductor using the 4- probe method, characteristics of a diode laser, Fabry-Perot etalon, Michelson and Mach-Zehnder interferometery, To visualize fine-splitting structure and verification of Bohr magneton value by Zeeman effect, characteristics of wave guides (optical fiber), determination of e/h ratio from Josephson junction experiments.

Electronics: Characteristics of FET & MOSFET, Experiments using OPAMP (IC-741) VIZ. (Inverting & non-inverting amplifier, Comparator, Summing and Differential Amplifier, Integrator & Differentiator, Frequency characteristics of various kind of filters), Introduction to logic gates and digital electronics, Study of Frequency and Amplitude modulation. Incubate student led experiments in consultation with a faculty/expert.

Statistical Mechanics [PH 507]

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Credit
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3 | 1 | 0 | 4

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Postulates of Thermodynamics; Conditions of thermal, mechanical and chemical equilibrium, examples; Maxwell relations, Thermodynamics stability; Statistical basis of thermodynamics, microscopic and macroscopic states. Classical ideal gas, Boltzman H theorem and irreversibility. Ergodic process; Micro canonical ensemble, counting of states and phase space volume; Canonical Ensemble, equilibrium between system and heat reservoir, canonical partition function, Helmholtz free energy, Grand canonical Ensemble, partition function, particle number and energy fluctuations; Quantum statistical ensemble theory: density matrix formulation; system of identical particles, manybody wavefunctions for non-interacting fermions and bosons; ideal quantum gases: Bose-Einstein statistics, Fermi-Dirac statistics; Bose systems, Bose Einstein Condensation (BEC ) in non-interacting gases. BEC in Interacting systems- experimental observation in Rb atoms; Photon gas, and thermodynamics of Blackbody radiation. Elementary excitations of liquid Helium –II; Ideal Fermi gas description, Paramagnetism and Landau diamagnetism, electron gas in metals, Specific heat of metals; Phase transitions, Condensation in Van der Waals gas, Ising model and Ferromagnetism. Landau Phenomenological theory; Non-Equilibrium statistical mechanics, Brownian motion, random walks, Langevin equation, Markov process.

Classical Mechanics [PH 508]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Review of elementary Newtonian mechanics: Mechanics of a particle, system of particles. Constrained motions, Virtual Work and D’Alembert’s Principle.

Lagrangian formulation of mechanics: Variational calculus, Hamilton’s principle, Generalized coordinates, Lagrange’s equations of motion, Symmetry and conservation theorems, Rotating frame of reference, illustrative examples and applications.

Central forces : Two body central force, equations of motion, first integrals, condition for closed orbits, Kepler’s problem, virial theorem, orbit of satellites, physics of tides.

Rigid body motion : Kinematics of rigid body motion: Euler Angles, Rotation matrices, Orthogonal transformations, Degrees of freedom of rigid body, Euler’s theorem, Inertial tensor, Energy and Angular momentum, Equations of motion, solution in torque free system, Gyroscopes, Precession of Satellite orbits, Precession of charged bodies in EM fields.

Hamilton’s equation of motions: Legendre Transformation, Hamilton function, Hamilton’s equations of motion, Liouville’s theorem, cyclic coordinates and conservation theorems, illustrative examples.

Lagrangian formulation for continuous systems: Transition from discrete to continuous systems, Lagrangian formulation of continuous systems, the stress-energy tensor and conservation theorems. Noether’s theorem.

Condensed Matter Physics [PH 509]

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Credit
L | T | P | C
3 | 1 | 0 | 4

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Condensed matter physics as study of many-body systems. Spatial correlations. Limitations of single particle quantum mechanics, role of interactions, effective approaches. Hartree and Hartree-Fock approximations; Crystalline solids, lattices, symmetries, reciprocal lattice, Bravais lattice, space groups. Liquid crystals and quasi crystals. Spatial correlations through electron, neutron, electromagnetic field scattering. Theory of scattering from crystals. X-Ray diffraction, correlation functions, structure factor; Crystal Vibrations. Phonons. Specific heat of solids, Debye and Einstein models. Anharmonic effects in crystals. Mössbauer effect; Electrons in solids, free electron theory of metals: free electron Fermi gas, semi-classical theory of conduction in metals, Hall effect, Electrons in a periodic potential, Bloch’s theorem, band structure, Brillouin zones, tight-binding model, effective mass, holes, insulators and semiconductors. Homogeneous semiconductors, semiconductor band structures, inhomogeneous semiconductors; Theory of nanostructures, electron in a one-dimensional array of potential wells, Quantum wires, wells and dots. Optical properties of nano structures; Quantum theory of diamagnetism and paramagnetism. Ferromagnetism. Order-disorder transitions. Curie point and exchange field. Concepts of Anti-ferromagnetism and frustration.

Condensed Matter Physics [PH 510]

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Credit
L | T | P | C
3 | 1 | 0 | 4

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Condensed matter physics as study of many-body systems. Spatial correlations. Limitations of single particle quantum mechanics, role of interactions, effective approaches. Hartree and Hartree-Fock approximations; Crystalline solids, lattices, symmetries, reciprocal lattice, Bravais lattice, space groups. Liquid crystals and quasi crystals. Spatial correlations through electron, neutron, electromagnetic field scattering. Theory of scattering from crystals. X-Ray diffraction, correlation functions, structure factor; Crystal Vibrations. Phonons. Specific heat of solids, Debye and Einstein models. Anharmonic effects in crystals. Mössbauer effect; Electrons in solids, free electron theory of metals: free electron Fermi gas, semi-classical theory of conduction in metals, Hall effect, Electrons in a periodic potential, Bloch’s theorem, band structure, Brillouin zones, tight-binding model, effective mass, holes, insulators and semiconductors. Homogeneous semiconductors, semiconductor band structures, inhomogeneous semiconductors; Theory of nanostructures, electron in a one-dimensional array of potential wells, Quantum wires, wells and dots. Optical properties of nano structures; Quantum theory of diamagnetism and paramagnetism. Ferromagnetism. Order-disorder transitions. Curie point and exchange field. Concepts of Anti-ferromagnetism and frustration.

Topics in Classical Mechanics and Electrodynamics [PH 605]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Lagrangian formulation of Classical mechanics; Principle of least action; Conservation laws and symmetries; Phase space formulation; Hamiltonian mechanics; Poisson brackets; Canonical transformations; Hamilton- Jacobi equation; Adiabatic invariants; Lagrangian and Hamiltonian formulation of Continuous systems and fields; Noether theorems; Gauge transformations; Local and Global symmetries; Review of Special relativity; Relativistic Mechanics of Charged Particle; Action principle for Electromagnetic field, Maxwell equations in covariant form; Electromagnetic energy momentum tensor; Propagation of Electromagnetic waves; Field due to a moving charge; Radiation reaction; Problem with Abraham-Lorentz formula; Limitations of Classical electrodynamics.

Topics in Quantum and Statistical Mechanics [PH 607]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Postulates of QM in bra-ket notation, entangled states, local hidden variable theory and classical and non- classical states; QM of composite systems, density matrix; Harmonic oscillator in operator representation, coherent states of harmonic oscillator; Addition of angular momenta; Symmetry in QM, concept of spin, SU(m) and SO(m) groups, geometric and dynamic symmetries, Runge-Lenz vector for Coulomb potential; Schrödinger equation in a periodic potential, energy spectrum of bulk and nano materials; Elements of the theory of scattering; Shannon and von Neumann entropies, statistical mechanical ensembles as the result of maximization of entropy with constraints; Spin and statistics, Maxwell-Boltzmann, Bose-Einstein, and Fermi distributions; Partition function, thermodynamic potentials in statistical mechanics, relationship between statistical and thermodynamic entropies; Bose-Einstein condensation.

Tools of Theoretical Physics [PH 608]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Tensors analysis in physics: Cartesian Tensors, Tensors in 4-dimensional space-time, Complex analysis: Analytic functions, Complex integration, Taylor and Laurent Series, Analytic continuation, Special functions: Hermite, Legendre, Laugerre polynomials and functions, Bessel functions, Spherical harmonics, Hypergeometric functions, confluent hypergeometric functions, Integral transforms: Fourier and Laplace transforms, Generalized functions: Dirac delta function, Generalized eigenfunction expansions, Green’s function for ordinary and partial differential operators, solutions of boundary values problems using Green’s function, Group theory in physics: Representation of a group, symmetry and degeneracy, Lie group and Lie algebra, Unitary and Orthogonal groups in physics

Introduction to Einstein’s Theory of General Relativity [PH 609]

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3 | 1 | 0 | 4

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Review of special relativity, uniformly accelerated observer, equivalence principle, gravitational redshift, gravity as the manifestation of space time curvature; Concept of differential manifold: Covariant derivative and connection, Lie derivative, space time metric, Christoffel symbols, Riemann curvature tensor, Ricci and Einstein tensors, Weyl tensor; Electrodynamics in curved space time; Hilbert action and Einstein’s field equation, Newtonian limit, energy conditions; Space time symmetries and Killing vector. Conserved quantities; Vacuum solution of general relativity, Schwarzschild metric, Birkhoff’s theorem, geodesics of Schwarzschild space time, Newtonian vs. relativistic orbits; Experimental test of general relativity: Bending of light, perihelion precession of Mercury, Shapiro time-delay; Weak field limit and linearised field equations, gravitational radiation, radiation by sources, energy loss. Introduction to post-Newtonian formulation.

Quantum Field Theory I [PH 610]

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Credit
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3 | 0 | 0 | 4

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Lorentz Invariance, Lorentz Group, Introduction to Spinors, Klein Gordan equation and Dirac equation, Limitations of relativistic quantum mechanics.

Scalar field theory, quantization and construction of the Fock space, Propagators. Complex scalar field, Antiparticles. Quantization of Dirac field, Spin Statistics theorem.

Interacting Field Theory, \lambda \phi^4 theory, Two point correlation function, Wick's Theorem, Interaction picture and Dyson series, Construction of Feynman Diagram.

Quantization of electromagnetic field, Gauge fixing, Introduction of QED, Feynman Rules and scattering cross sections of tree level processes.

X-ray Scattering: Concepts and Applications [PH 611]

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Credit
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3 | 0 | 0 | 4

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X-rays and their interaction with matter, scattering and absorption cross section, refraction and reflection; Sources: X-ray tubes, advent of synchrotron radiation; Refraction and reflection from surfaces and interfaces: refractive index including absorption, Snell’s law and the Fresnel equations in the X-ray region; Kinematical scattering I: non-crystalline materials: scattering from an atom, molecule, liquids and glasses, small-angle X-ray scattering (SAXS); Kinematical scattering II: crystalline order, scattering from a crystal, quasiperiodic structures, crystal truncation rods, lattice vibrations, Debye-Waller factor and Thermal Diffuse Scattering, applications of kinematical diffraction; Diffraction by perfect crystals: kinematical reflection from a few layers, Darwin theory and dynamical diffraction; Diffuse scattering: correlation functions, Born approximation; Applications of X-ray scattering: surface X-ray scattering techniques like X- ray reflectivity (XRR), grazing incidence X-ray diffraction (GIXD), grazing incidence small angle X-ray scattering (GISAXS), photoelectric absorption, resonant scattering.

Quantum Field Theory II [PH 612]

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Credit
L | T | P | C
3 | 1 | 0 | 4

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Lorentz Invariance, Lorentz Group, Introduction to Spinors, Klein Gordan equation and Dirac equation, Limitations of relativistic quantum mechanics.

Scalar field theory, quantization and construction of the Fock space, Propagators. Complex scalar field, Antiparticles. Quantization of Dirac field, Spin Statistics theorem.

Interacting Field Theory, \lambda \phi^4 theory, Two point correlation function, Wick's Theorem, Interaction picture and Dyson series, Construction of Feynman Diagram.

Quantization of electromagnetic field, Gauge fixing, Introduction of QED, Feynman Rules and scattering cross sections of tree level processes.

Atomic and Molecular Physics [PH 614]

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Credit
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3 | 0 | 0 | 4

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Schrödinger equation for one-electron atoms, energy levels, eigenfunctions of the bound state, expectation values. The electromagnetic field and its interaction with one electron systems, The dipole approximation. Einstein’s coefficients. Selection rules, lifetimes of excited states. Line shapes and widths. Fine structure of hydrogenic atoms. Spectral terms. The Zeeman effect. The Stark effect. The lamb shift. Hyperfine structure and isotope shifts.

Two-electron atoms. Spin wave functions and the Pauli exclusion principle. Level scheme of Helium atom. The ground and excited states of two-electron atoms. Approximation methods. Auger effect.

Many-electron atoms. The central field approximation. Thomas-Fermi model. Slater determinant. The Hartree-Fock method and the self-consistent field. Corrections to the central field approximation. L-S and j-j coupling. X-ray spectra.

Molecular structures and spectra. Born-Oppenheimer approximation, Rotational and vibrational spectra of diatomic molecules. Structure of polyatomic molecules. Raman Scattering. Electronic spectra. The Frank Condon principle. Raman Spectroscopy.

Physics of two-dimensional materials [PH 615]

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Credit
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3 | 0 | 0 | 4

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Introduction: Classification of materials based on dimensions, 2D material family, History, Hexagonal crystal structure, Structural stability, Superlative properties.

Synthesis of 2D materials: Micromechanical exfoliation, Chemical vapor deposition, Liquid exfoliation, van der Waals epitaxy.

Characterization methods: Microscopy techniques (AFM, TEM), Raman spectroscopy, PL spectroscopy, X-ray diffraction.

Electronic properties and devices: Band structure of graphene, Tight-binding approach, Effective mass, Dirac Fermions, Density of states, Band structure of bilayer graphene, MoS 2 , WS 2 , Field effect transistor (FET) with 2D materials, High frequency transistors, Klein tunneling, Schottky interface, p-n junctions, Heterostructures, Quantum Hall effect. Optical properties: Light-matter interactions, Fine structure constant, Optical conductivity, Thickness dependent optical properties, van Hove singularity, Plasmons, Excitons and Trions

Chemical properties: Hybridization, Functionalization, Hydrogenation, Graphane, Flourographene, Adsorption characteristics

Mechanical properties: Tensile strength, Young’s modulus, Bendability, Mermin-Wagner Theorem, Mechanical resonators

Thermal properties: Thermal conductivity, Weidman-Franz law, Thickness dependency, Thermoelectric power-Seebeck effect, Nernst effect

Membrane science: 2D laminates, Nanopores, Nanochannels, Desalination, Ion sieving, Blue energy, DNA sequencing

Future Perspective and Applications: Lightweight transparent coatings, Flexible displays, Solar cells, Heterostructure based devices, Tunneling transistors, Light emitting diodes, Super capacitors, Sensors, Composites, Future prospects

Quantum Optics [PH 616]

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Credit
L | T | P | C
3 | 0 | 0 | 4

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Hamiltonian of free classical electromagnetic (e.m.) field. The concept of field mode. The e.m. field quantization, Coherent and squeezed states of the field. Wigner Functions, the Glauber-Sudarshan P- function and the concept of classical and non-classical states of the e.m. field.

Classical atomic dipole – e.m. field interaction, Polarizability, Damping, Dipole Radiation, Mechanical effects of light on atoms – dipole force/optical tweezers/laser cooling

Hamiltonian of a free atom. Atomic dipole moment in terms of atomic eigenstates.

Classical e.m. field, Two and three-level atoms, interaction Hamiltonian in dipole approximation and Rotating Wave Approximation (RWA). Atomic dynamics in single mode classical field.

Optical Bloch equations for damped atomic dynamics. The concept of Density Matrix. Two-time correlation functions; absorption and emission spectrum (resonance fluorescence) of scattered radiation from atoms. Mechanical effects of light on the two-level atom, dressed states.

Two level interacting with single mode quantized field: Jaynes-Cummings model.

Quantum Theory of Damping: Atoms in a thermal field: master equation for two-level atoms and the origin of the spontaneous decay of an excited state and the Einstein-A coefficient.

Quantum Computing and Information [PH 643]

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Credit
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3 | 0 | 0 | 4

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Why quantum computing. Review of postulates of quantum mechanics. Concept of a qubit and its practical realization. Bloch sphere representation of a qubit. Algebra of one and two qubit states and operators. Schmidt decomposition of pure states of two qubits. Quantum gates and circuits. Hamiltonians for implementing gates and their physical realization. Universal quantum gates. Implementing arbitrary n-qubit gates in terms of universal gates.

Quantum Fourier transform. Quantum computing algorithms: Deutsch algorithm, Deutsch- Jozsa algorithm, refined Deutsch-Jozsa algorithm, Bernstein-Vazirani algorithm, Grover’s search algorithm, algorithm for finding period of a function, and Shor’s factorization algorithm.

Error correction in quantum computing.

Fundamental differences between classical and quantum mechanics based on the concepts of entanglement and separability, and highlighted by Schrödinger’s Cat paradox, and Einstein, Podolosky, Rosen (EPR) paradox. Local hidden variable theory. Concept of classical and non-classical states and exclusive quantum effects. Bell like inequalities and other approaches to identify non-classical states.

Why quantum information. Dense coding, quantum teleportation, quantum cryptography.

Classical information and Shannon entropy as a measure of information. Shannon’s noiseless channel coding theorem. Classical joint, conditional, and mutual information.

Density matrix. Quantum information and von Neumann entropy. Problem of communicating quantum states and fidelity. Schumacher’s quantum noiseless coding theorem. Mutual information in quantum theory. Measures of quantumness of mutual information: quantum discord, measurement induced disturbance, symmetric discord, and local hidden variables theoretic measure of quantumness of mutual information.

Tools of Experimental Physics [PH 644]

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Credit
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3 | 0 | 1 | 4

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Essentials of data analysis: Uncertainties in measurement, propagation of errors, probability distributions, rejection of data, least-squares fitting, the chi-squared test.

Structure analysis techniques: Overview of X-ray, neutron and low energy electron diffraction methods. Demonstration of XRD and data analysis.

Electrical and magnetic characterization: Resistivity studies, Classical & Quantum Hall effect; principle & experimental measurement, Magnetic Susceptibility, low Current & Voltage measurements, Demonstration of Hall Effect and resistivity measurement set up, Principles of vibrating-sample magnetometer and superconducting quantum interference device.

Vacuum technology and deposition methods: Generation and measurement of low pressure, evaporation and sputtering techniques. Demonstration of relevant experimental set up.

Spectroscopy and Microscopy techniques: Raman spectroscopy, X-ray photoelectron spectroscopy (XPS/UPS). Overview of Nuclear Magnetic Resonance Spectroscopy and Electron Spin Resonance Spectroscopy. Basic principles & Measurements. scanning electron microscopy, Rutherford backscattering, scanning probe microscopy, transmission electron microscopy and atomic force microscopy. Demonstration of NMR. AFM, and TEM.

Topics in Soft and Active Matter Physics [PH 645]

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Credit
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3 | 0 | 0 | 4

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Introduction and Overview: Definition and classification of soft matter. Energies and timescales.

Intermolecular and Surface Forces: Thermodynamic and statistical aspects of intermolecular forces, Interactions involving polar molecules, Van der Waals forces, Repulsive steric forces, Forces between particles and surfaces, Thermodynamic principles of self-assembly, Interactions of Biological Membranes and Structures.

Dynamics of Molecules: Diffusion, permeation and flow, Smoluchoski’s relation, Onsager reciprocal relations.

Essentials of Polymer: Microstructures, fractal nature of polymer conformations, Ideal chain models, free energy, excluded volume and self- avoiding walks, Flory theory, structure and functions of proteins.

Colloidal Assemblies: Electrostatics, Poisson-Boltzmann equation, Debye-Huckel theory, Derjaguin approximation, hydrodynamics, Diffusion limited aggregation, Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, Depletion forces, electrokinetic processes.

Active Matter: Definition and examples. Physics at low Reynolds number, Biomolecular motors, dynamics of bacterial suspensions, chemically powered systems, behavior of single and multiple swimmers, emergent dynamics, activity induced propulsion and processes under cytosolic conditions.