Courses Description

Vector algebra, Motion of Particle in one, two and three dimensions, Projectile motion, Uniform Circular motion, Force , mass, Newton’s laws, Tension and Normal force, Frictional forces, Concept of free body diagram, Electrostatic force, electrostatic field, Electric dipole, Electric flux, Gauss ‘s law, Electrostatic potential, magnetic field, Biot-Savart law, Effect of magnetic field on current carrying conductors, Ampere’s Law, How magnetism is used in a computer, Band theory, Insulators, metals, semiconductors, doped semiconductors, The p-n junction, The junction rectifier, LED, Transistor.

Vector algebra, Motion in two and three dimensions, Force and motion, Newton’s laws, Application of Newton’s second law for some specific forces, Friction, Rotation, Moment of inertia, Torque, Rotational Energy, Simple Harmonic Motion, Waves, Waves speed, Energy and Power of traveling waves, Doppler’s effect. Electrostatic force, electrostatic field, Electric dipole, Electric flux, Gauss ‘s law, Electrostatic potential, magnetic field, Biot-Savart law, Effect of magnetic field on current carrying conductors, Ampere’s Law, Magnetic dipole, Faraday’s law of electromagnetic induction, Energy stored in electric and magnetic fields, Introduction to solid state Physics, Superconductivity, Semiconductors and Modern trends in Atomic Physics.

Vector and Scalars, Motions in 2 and 3 dimensions, projectile motion, uniform circular motion, Force and acceleration, Newton’s laws, frictional force, Work, Energy, Kinetic and Potential Energy, Gravitational force, Conservation of energy, Rotational motion, Angular velocity, Torque, Rotational Inertia, Oscillations, Simple Harmonic motion, Harmonic Oscillator, Waves, Transverse and Longitudinal waves, Wave speed, Energy and Power of Waves, Standing Waves. Inertial and non-inertial frame, Postulates of Relativity, The Lorentz Transformation, Relativity of time, Relativity of length, Relativity of mass, Transformation of velocity, variation of mass with velocity, mass energy relation and its importance, relativistic momentum and Relativistic energy.

Electric charge, Coulomb's Law, Electric field, electric flux, Gauss's Law, Electric potential, Capacitors, Electric current, Ohm's law, Magnetic fields, Ampere's Law, Inductors, Faraday's Law, DC Circuits, Energy stored in magnetic fields, magnetic materials, induced magnetic fields. The Electromagnetic Model, Vector Analysis, Static Electric Fields, Solution of Electrostatic Problems, Steady Electric Currents. Electromagnetic waves, Poynting vector, Interference, Diffraction. Alternating Fields and Currents, Diamagnetism, Paramagnetism, Ferromagnetism, Hysteresis.

Basic Concepts and Definitions in Thermodynamics: Thermodynamic system, Surrounding and Boundaries. Type of systems, Macroscopic and microscopic description of system, Heat and Temperature: Temperature, Kinetic theory of ideal gas, Work done on an ideal gas, First law of thermodynamics and its applications to adiabatic, isothermal, cyclic and free expansion. Reversible and irreversible processes, Second law of thermodynamics, Carnot theorem and Carnot engine. Heat engine, Entropy and Second law of thermodynamics, Entropy and Probability, Thermodynamic Functions: Thermodynamic functions, Introduction to Statistical Mechanics, Mean free path and microscopic calculations of mean free path. Distribution of Molecular Speeds, Distribution of Energies, Maxwell distribution, Maxwell Boltzmann energy distribution

Simple and Damped Simple Harmonic Oscillation, Mass-Spring System, Simple Harmonic Oscillator Equation, Complex Number Notation, LC Circuit, Simple Pendulum, Quality Factor, LCR Circuit. Forced Damped Harmonic Oscillation, Coupled Oscillations, Transverse Waves, Longitudinal Waves, Traveling Waves, Standing Waves in a Finite Continuous Medium, Traveling Waves in an Infinite Continuous Medium, Energy Conservation, Transmission Lines, Reflection and Transmission at Boundaries, Electromagnetic Waves. Wave Pulses: Multi-Dimensional Waves, Interference and Diffraction of Waves

Motivation for Non--Classical Physics, Wave-Particle Duality, Quantum Mechanics in One Dimension

Quantum Mechanical Tunneling, Photoelectric effect, Compton effect, production and properties of X-rays, diffraction of X-rays, concept of matter waves, deBroglie relationship, The concept of a wave function, time independent Schrodinger equation and interpretation of the equation, solving the Schrodinger equation for a free particle, Concept of tunneling, reflection and transmission of wave functions from barriers The Hydrogen atom, orbitals, angular momentum and its quantization, orbital magnetism, Zeeman effect, concept of spin, Pauli’s exclusion principle, Building of the periodic table, Quantum Mechanics in Three Dimensions: , From Atoms to Molecules and Solids: Ionic bonds, covalent bonds, hydrogen bonds, Nuclear Structure: Size and structure of nucleus, nuclear forces,

Review of Newtonian Mechanics: Frame of reference, orthogonal transformations, angular velocity and angular acceleration, Newton’s laws of motion, Galilean transformation, conservation laws, The Motion of Rigid Bodies: The Euler angles, rotational kinetic energy and angular momentum, the inertia tensor, Euler equations of motion, motion of a torque-free symmetrical top, Central Force Motion: The two-body problem, effective potential and classification of orbits, Kepler’s laws, Motion in Non-inertial Systems: Accelerated translational co-ordinate system, dynamics in rotating co-ordinate system, The Lagrange Formulation of Mechanics and Hamilton Dynamics: Generalized co-ordinates and constraints, D’Alembert’s principle and Lagrange’s Equations, Hamilton’s principle, integrals of motion, nonconservative system and generalized potential

The Dirac Delta Function: Review of vector calculus using example of Dirac Delta function, Electrostatics: The electric field: introduction, Coulomb’s law, the electric field, continuous charge distributions. Divergence and curl of electrostatic fields: field lines, flux and Gauss’s law, the divergence of E, applications of Gauss’s law, the curl of E. Electric potential: introduction to potential, comments on potential, Poisson’s equation and Laplace’s equation. The Method of Images, Multi-pole Expansion: Polarization: dielectrics, induced dipoles, alignment of polar molecules, polarization, Magnetostatics: The Lorentz Force law: magnetic fields, magnetic forces, currents. The Biot-Savart Law: steady currents, the magnetic field of a steady current. Magnetic Fields in Matter: Magnetization, diamagnets, paramagnets, ferromagnets, torques and forces on magnetic dipoles, effect of a magnetic field on atomic orbits, magnetization.

Review of vector analysis: definitions, Differential operators, gradient, divergence, curl, integration of vector fields, Gauss' theorem, Stokes' theorem, Gauss' law, Poisson's equation

Vector analysis in curvilinear coordinates, orthogonal coordinates Determinants, matrices, orthogonal and unitary matrices, matrix diagonalization Finite and infinite sequences, limit of a sequence Fourier series and analysis, use and application to physical systems Complex algebra, functions of a complex variable, Cauchy-Riemann conditions, integration of complex

The crystal lattice, basic quantum mechanics, energy bands, elemental semiconductors, compound semiconductors, alloys, semiconductors electrons, holes, density-of-states, effective mass, carrier concentration, doping, recombination, the Fermi energy, quasi-Fermi energies, mobility, conductivity, Hall effect, optical properties of semiconductors, carrier drift and diffusion. Diodes (pn junction, Schottky, LED’s, laser diodes, solar cells and photodiodes), bipolar transistors, field effect transistors: JFET’s, MESFETs, MODFETs and MOSFET’s.

Historical motivation: wave-particle duality, photo-electric effect, instability of atoms, black body catastrophe. Observables and operators, postulates of mechanics, measurement problems, the state function and expectation values, Schrödinger wave equation, Time-independent Schrödinger equation and one-dimensional problems, stationary states, superposition principle, free particles, infinite and finite square well, harmonic oscillator, and delta-function potential. Hilbert space, Dirac notation, linear transformations, discrete and continuous basis vectors, hermitian and unitary operators, Waves incident on potential barrier, reflection and transmission coefficients, WKB method. Quantum mechanics in three-dimensions, cartesian and spherical forms of Schrodinger equation, separation of variables, Rotational symmetry, angular momentum as a generator of rotations, spherical harmonics and their properties. Completeness and orthonormality properties.

Ohm’s law, Kirchoff’s voltage and current laws, the superposition principle, Source transformation, maximum power transfer theorem, Thevenin-Norton equivalent circuits, linear system analysis basics. Introduction to semiconductors, intrinsic and extrinsic semiconductors, Ideal diodes, terminal characteristics of junction diodes, Basic principles of pn junctions, built-in potential, Bipolar Junction Transistors (BJT),, Basic operational amplifiers inverting and non-inverting, differential modes, gain and bandwidth, frequency response Principles of feedback

Electrodynamics: Electromotive force: Ohm’s law, electromotive force, motional emf, electromagnetic induction: Faraday’s law, Conservation Laws: Charge and energy: the continuity equation, Poynting’s theorem, momentum: Newton’s third law in electrodynamics, Electromagnetic Waves: Waves in one dimension: the wave equation, sinusoidal waves, boundary conditions, reflection and transmission, polarization Potentials and Fields: The potential formulation: scalar and vector potentials, gauge transformations, Coulomb gauge and Lorentz gauge, Radiation, Dipole Radiation: What is radiation, electric dipole radiation, magnetic dipole radiation, radiation from an arbitrary source, Electrodynamics and Relativity: The special theory of relativity: Einstein’s postulates, the geometry of relativity, the Lorentz transformations

Vector spaces, basis vectors, linear independence, function spaces. Review of differentiation and integration, continuity and differentiability, firstorder differential equations, general solution by integration, uniqueness property. Second order differential equations with constant coefficients, Euler linear equations, singular points, series solution by Frobenius' method, Second order linear partial differential equations, Laplace equation, wave equation, solution of Poisson equation, Definition of probability, simple properties, random variables, binomial distribution, Poisson and Gaussian distributions, central limit theorem, statistics.

Motion of a particle in a central potential. Separation of variables, effective potential, solution for the Coulomb problem.Spin as an internal degree of freedom, intrinsic magnetic moment, Identical particles: Many-particle systems, system of distinguishable noninteracting particles, systems of identical particles, Scattering: Classical scattering theory, The variational principle: Variational theorem, variational approximation method, the ground state of helium atom.The WKB approximation: WKB wave functions, Time-dependent perturbation theory, Time-independent perturbation theory: Nondegenerate perturbation theory, degenerate perturbation theory.

Crystal Structure: Lattices and basis, Symmetry operations, Fundamental Types of Lattice, Position and Orientation of Planes in Crystals, Simple crystal structures, Crystal Diffraction and Reciprocal Lattice: Diffraction of X-rays, Neutrons and electrons from crystals; Bragg’s law; Reciprocal lattice, Ewald construction and Brillouin zone, Fourier Analysis of the Basis., Phonons and Lattice, Thermal Properties of Solids: , Electrical Properties of Metals: Classical free electron theory of metals, energy levels and density of orbital’s in one dimension, effect of temperature on the Fermi–Dirac distribution function, properties of the free electron gas, electrical conductivity and Ohm’s Law,

One Electron Atoms: Review of Bohr Model of Hydrogen Atom, Reduced Mass, Atomic Units and Wavenumbers, Energy Levels and Spectra, Schrodinger Equation for One-Electron Atoms, Quantum Angular Momentum and Spherical Harmonics, Electron Spin, Spin-Orbit interaction. Levels and Spectroscopic Notation, Lamb Shift, Hyperfine Structure and Isotopic Shifts. Rydberg Atoms. Interaction of One-Electron Atoms with Electromagnetic Radiation: Radiative Transition Rates, Dipole Approximation, Einstein Coefficients, Selection Rules, Dipole Allowed and Forbidden Transitions. Metastable Levels, Line Intensities and Lifetimes of Excited States, Shape and Width of Spectral Lines, Scattering of Radiation by Atomic Systems, Zeeman Effect, Linear and Quadratic Stark Effect. Many-Electron Atoms: Schrodinger Equation for Two-Electron Atoms, Para and Ortho States, Pauli’s Principle and Periodic Table, Coupling of Angular Momenta, L-S and J-J Coupling. Ground State and Excited States of Multi-Electron Atoms, Configurations and Terms. Molecular Structure and Spectra: Structure of Molecules, Covalent and Ionic Bonds, Electronic Structure of Diatomic Molecules, Rotation and Vibration of Diatomic Molecules, Born-Oppenheimer Approximation. Electronic Spectra, Transition Probabilities and Selection Rules, Frank- Condon Principle, H2+ and H2. Effects of Symmetry and Exchange. Bonding and Anti-bonding Orbitals. Electronic Spin and Hund’s Cases, Nuclear Motion: Rotation and Vibrational Spectra (Rigid Rotation, Harmonic Vibrations). Selection Rules. Spectra of Triatomic and Polyatomic Molecules, Raman Spectroscopy, Mossbauer Spectroscopy

History: Starting from Bacqurel’s discovery of radioactivity to Chedwick’s neutron.

Basic Properties of Nucleus: Nuclear size, mass, binding energy, nuclear spin, magnetic dipole and electric quadrupole moment, parity and statistics. Nuclear Forces: Yukawa's theory of nuclear forces. Nucleon scattering, charge independence and spin dependence of nuclear force, isotopic spin. Nuclear Models: Liquid drop model, Fermi gas model, Shell model, Collective model.

Theories of Radioactive Decay: Theory of Alpha decay and explanation of observed phenomena, measurement of Beta ray energies, the magnetic lens spectrometer, Fermi theory of Beta decay, Neutrino hypothesis, theory of Gamma decay, multipolarity of Gamma rays, Nuclear isomerism.

Nuclear Reactions: Conservation laws of nuclear reactions, Q-value and threshold energy of nuclear reaction, energy level and level width, cross sections for nuclear reactions, compound nucleolus theory of nuclear reaction and its limitations, direct reaction, resonance reactions, Breit-Wigner one level formula including the effect of angular momentum

Review of Classical Thermodynamics: States, macroscopic vs. microscopic, "heat" and "work", energy, entropy, equilibrium, laws of thermodynamics, Equations of state, thermodynamic potentials, temperature, pressure, chemical potential, thermodynamic processes (engines, refrigerators), Maxwell relations, phase equilibria. Foundation of Statistical Mechanics: Phase Space, Trajectories in Phase Space, Conserved Quantities and Accessible Phase Space, Macroscopic Measurements and Time Averages, Ensembles and Averages over Phase Space, Liouville's Theorem, and examples (e.g. adsorption), calculation of partition function and thermodynamic quantities. Simple Applications of Ensemble Theory: Monoatomic ideal gas in classical and quantum limit, Gibb’s paradox and quantum mechanical enumeration of states, equipartition theorem and examples (ideal gas, harmonic oscillator), specific heat of solids, quantum mechanical calculation of para-magnetism, Quantum Statistics.

Dielectric Properties of Solids: Polarization, Depolarization, Local and Maxwell field, Lorentz field, Clausius-Mossotti relation, Dielectric Constant and Polarizability, Masurement of dielectric constant, ferro electricity and ferroelectric crystals, Phase Transitions, First and 2nd order phase transitions, Applications Semiconductors: General properties of semiconductors, intrinsic and extrinsic semiconductors, their band structure, carrier statistics in thermal equilibrium, band level treatment of conduction in semiconductors and junction diodes, diffusion and drift currents, collisions and recombination times Optical Properties: Interaction of light with solids, Optical Properties of Metals and Non-Metals, Kramers Kronnig Relation, Excitons, Raman Effect in crystals, optical spectroscopy of solids. Magnetic Properties of Materials: Magnetic dipole moment and susceptibility, different kinds of magnetic materials, Langevin diamagnetic equation, Paramagnetic equation and Curie law, Classical and quantum approaches to paramagnetic materials. Ferro-magnetic and anti – ferromagnetic order, Curie point and exchange integral, Effect of temperature on different kinds of magnetic materials and applications. Superconductivity: Introduction to superconductivity, Zero-Resistance and Meissner Effect.

Review of Number Systems: Binary, Octal and Hexadecimal number system, their inter-conversion, concepts of logic, truth table, basic logic gates. Boolean Algebra: De Morgan’s theorem, simplification of Boolean expression by Boolean Postulates and theorem, K-maps and their uses. Don’t care condition, Different codes. (BCD, ASCII, Gray etc.). Parity in Codes. IC Logic Families: Basic characteristics of a logic family. (Fan in/out, Propagation delay time, dissipation, noise margins etc. Different logic based IC families (DTL, RTL, ECL, TTL, CMOS). Combinational Logic Circuit: Logic circuits based on AND – OR, OR-AND, NAND, NOR Logic, gate design, addition, subtraction (2’s compliments, half adder, full adder, half subtractor, full subtractor encoder, decoder, PLA. Exclusive OR gate. Sequential Logic Circuit: Flip-flops clocked RS-FF, D-FF, T-FF, JK-FF, Shift Register, Counters (Ring, Ripple, up-down, Synchronous) A/D and D/A Converters. Memory Devices: ROM, PROM, EAPROM, EE PROM, RAM, (Static and dynamic) Memory mapping techniques Micro Computers: Computers and its types, all generation of computers,

Computer Languages: A brief introduction of the computer languages like Basic, C. Pascal etc. and known software packages of computation Numerical Methods: Numerical Solutions of equations, Regression and interpolation, Numerical integration and differentiation. Error analysis and technique for elimination of systematic and random errors Modeling & Simulations: Conceptual models, the mathematical models, Random numbers and random walk, doing Physics with random numbers, Computer simulation, Relationship of modeling and simulation. Some systems of interest for physicists such as Motion of Falling objects, Kepler's problems, Oscillatory motion, Many particle systems, Dynamic systems, Wave phenomena, Field of static charges and current, Diffusion, Populations genetics etc

Guided Wave Optics: Planar slab waveguides, Rectangular channel waveguides, Single and multi-mode optical fibers, waveguide modes and field distributions, waveguide dispersion, pulse propagation Gaussian Beam Propagation: ABCD matrices for transformation of Gaussian beams, applications to simple resonators Electromagnetic Propagation in Anisotropic Media: Reflection and transmission at anisotropic interfaces, Jones Calculus, retardation plates, polarizers Electro-optics and Acousto-optics: Linear electro-optic effect, Longitudinal and transverse modulators, amplitude and phase modulation, Mach-Zehnder modulators, Coupled mode theory, Optical coupling between waveguides, Directional couplers, Photoelastic effect, Acousto-optic interaction and Bragg diffraction, Acousto-optic modulators, deflectors and scanners Optoelectronics: p-n junctions, semiconductor devices: laser amplifiers, injection lasers, photoconductors, photodiodes, photodetector noise.

Introduction to nanomaterials is an introductory course to the students intending to do specialization in nanoscience and nanotechnology. The course includes the brief introduction of nanomaterials, the properties of nanomaterials and their comparison to the bulk materials. The synthesis of nanoparticles of different dimensionalities will be thoroughly discussed. The last section includes the applications of nanomaterials and the safety measurements against toxicity of materials. An introduction to nanoscience and nanotechnology: Historical perspective, physical properties of bulk and nano-sized nanostrucutres, surface energy, nucleation and growth of nanostrucutres, stabilization of nanoparticles, synthesis methods for zero, one and two dimensional nanostructures, discussion of methods, superlattices, self-assembly, Thiol-derivatised monolayer, monolayers of acids, amines and alcohols, Langmuir-Blodgett films, electrochemical deposition lithography techniques, top-down and bottom-up approaches, physical vapor deposition, chemical vapor deposition, sputtering, applications of nanoparticles, material safety and application

Semiconductor Fundamentals: Composition, purity and structure of semiconductors, energy band model, band gap and materials classification, charge, effective mass and carrier numbers, density of states, the Fermi function and equilibrium distribution of carriers, doping, n and p-type semiconductors and calculations involving carrier concentrations, EF etc., temperature dependence of carrier concentrations, drift current, mobility, resistivity and band bending, diffusion and total currents, diffusion coefficients, recombination-generation, minority carrier life times and continuity equations with problem solving examples. Device Fabrication Processes: Oxidation, diffusion, ion implantation, lithography, thin-film deposition techniques like evaporation, sputtering, chemical vapour deposition (CVD), epitaxy etc. PN Junction and Bipolar Junction Transistor: Junction terminology, Poisson’s equation, qualitative solution, the depletion approximation, quantitative electrostatic relationships, ideal diode equation, non-idealities, BJT fundamentals, Junction field effect transistor, MOS fundamentals, the essentials of MOSFETs. Dielectric Materials: Polarization mechanisms, dielectric constant and dielectric loss, capacitor dielectric materials, piezoelectricity, ferroelectricity and pyroelectricity

Brief introduction of nanoparticles, its scope , magnetic nanoparticles inside and everywhere around , most extensively studied magnetic nanoparticles and their preparation, metals, nanoparticles of rare earth metals, oxidation of metallic nanoparticles, magnetic alloys , Fe–Co alloys, magnetic oxides, magnetic moments and their interactions with magnetic fields. Bohr magneton, spin and orbital magnetic moments, magnetic dipole moments in an external magnetic field, the spontaneous magnetization, anisotropy, domains, the spontaneous magnetization, temperature dependence of the magnetization in the molecular field approximation, Curie temperature in the Weiss Heisenberg model curie temperature in the stoner model, the meaning of exchange in the Weiss Heisenberg and stoner models, thermal excitations: spin waves, the magnetic anisotropy, the shape anisotropy ,the magneto-crystalline anisotropy. Magnetic microstructure: magnetic domains and domain walls, ferromagnetic domains, antiferromagnetic domains, magnetization curves and hysteresis loops

The brief introduction of structure of surfaces, defects, interaction of defects and their observation, electronic states, charge distribution at surfaces, elasticity theory of surface defects, thermodynamics of flat and curved surfaces, statistical theromodynamics i.e. the free energy, vapor pressure of solid surfaces, adsorption of molecules and ions, desorption, chemical bonding, surface phonons, adsorbate modes, inelastic scattering of atoms and electrons, optical techniques for scattering observations electronic, optical and magnetic properties of surfaces and the diffusion phenomenon.

Overview of characterization techniques, light microscopy, Scanning Electron Microscopy (SEM), Scanning Tunneling Microscopy (STM), Particle Size Analyzer, Transmission Electron Microscopy (TEM) , Scanning Force Microscopy (SFM), Energy-Dispersive X-Ray Spectroscopy (EDS), Electron Energy-Loss Spectroscopy in the Transmission Electron Microscope, Scanning Transmission Electron Microscopy (STEM), XRD. Experimental methods for structure determination-X-rays, properties of X-rays, diffraction of X-rays, experimental methods and crystal determination techniques, X-Ray Photoelectron Spectroscopy (XPS), Photoluminescence (PL) and Fourier Transform Infrared Spectroscopy (FTIR), Raman Spectroscopy, Solid State Nuclear Magnetic Resonance (NMR) and Hall Effects (electrical properties measurements).

Overview of quantum mechanics, electrons in a crystal field, Electrical properties: band theory of metals and semiconductors, Fermi energy, density of states, effective mass, conductivity of electrons in metals and semiconductors – classical and quantum mechanical treatment, conduction in polymers, metal oxides, dielectric properties, ferrroelectricity, piezoelectricity, Electronic properties: free electrons with and without damping, reflectivity, Lorentz equations, Harmonic oscillators, optical spectra of materials conduction and dispersion, Magnetic properties: Curie law, Langevin theory of para- and dia-magnetism, molecular field theory, Heisenberg exchange interaction, Weiss field, point-charge approximation, crystal fields, field induced and 4f electron anisotropy, Magnetic properties: Origin of atomic moments, paramagnetism of free ions, Brillouin function, Curie law, Langevin theory of para- and dia-magnetism, molecular field theory, Heisenberg exchange interaction, Weiss field, point-charge approximation, crystal fields, field induced and 4f electron anisotropy, Caloric effects, magnetic anisotropy permanent magnets, domain walls, coercivity, hysteresis loop, exchange coupling in rare-earth magnets, hard ferrites, soft magnetic materials, random-anisotropy model, soft magnetism and grain size, Heat capacity, classical theory, Debye model, Einstein model, electronic contribution, thermal conduction in metals and alloys (classical and quantum consideration), thermal conduction of dielectrics, electrical, optical and magnetic properties in nano regime

Quarks and leptons, Yukawa and electromagnetic interactions, weak, strong and gravitational interactions, current conservation in the Maxwell’s equations, Lorentz and gauge invariance in electromagnetism, the Klein-Gordon equation, the Dirac equation, Lorentz transformation of spinors, solutions of the Dirac equation, electromagnetic interactions via gauge principle, the quantum field, Lagrangian and Hamiltonian formalism, relativity, mass and four dimensions, qualitative introduction to interactions, the interaction picture and S-matrix, the decay and scattering amplitude, the Yukawa exchange, the complex scalar field, the Dirac field and the spin statistics, Coulomb scattering of spin 0 and spin 1/2 particles, spin 0 and spin 1/2 scattering, electron-pion scatterings crossing symmetry, Compton scattering, electron-muon scattering, electron-proton elastic and inelastic scattering, the parton model, the quark parton model, the Drell-Yan process, electron-positron annihilation into hadrons.

Introduction to plasmas, how plasmas are produced, Debye length, plasma frequency, number of electrons in a Debye sphere, the de-Broglie wavelength and quantum effects, representative plasma parameters. Motion of a charged particle in a static uniform magnetic field and in the presence of perpendicular electric and magnetic fields, gravitational drift, gradient and curvature drifts. Motion in a magnetic mirror field, drift-motion in a time varying electric and magnetic fields, adiabatic invariants, conservation of J in time independent fields, the Hamiltonian method and chaotic orbits. Fluid equations for a plasma, continuity equation, momentum balance equation, equation of state, and two-fluid equations. Waves in cold plasma, Fourier representation of waves, plasma oscillations, electron and ion waves, sound waves, electrostatic ion waves perpendicular to magnetic field, lower-hybrid frequency. Electromagnetic waves for unmagnetized and magnetized plasmas, Alfven waves, magnetosonic waves, and ray paths in inhomogeneous plasmas. Introduction to controlled fusion: Basic nuclear fusion reactions, reaction rates and power rates and power density, radiation losses from plasmas, operational conditions.

Correspondences and transformations, groups, definitions and examples, subgroups, Cayley's theorem, Cosets, Lagrange's theorem, conjugate classes, invariant subgroups, factor groups, homomorphism, direct products, quick review of linear vector spaces, group representations, equivalent representations - characters, construction of representations, invariance of functions and operators, operators, unitary representations, Hilbert space Reducibity/irreducibility of a representation, Schur's Lemmas, Lie groups, isomorphism, subgroups, mixed continuous groups, one parameter group, structure constants, Lie algebras, compact semisimple Lie groups, linear representations, invariant integration, irreducible representations, the Casimir operator, universal covering group, systems of identical particles and SU(n), angular momentum analysis, the Pauli principle, seniority in atomic spectra, atomic spectra in jj-coupling, isotopic spin, nuclear spectra in L-S coupling, the L-S and jj-coupling shell model.

Review of quantum mechanics, Dirac’s notation, Pauli spin matrices, electromagnetic waves and photons, wavelength and frequencies of electromagnetic radiation. Spontaneous and stimulated emission, absorption. Maser principle, cavity, gain medium, population inversion, Boltzmann statistics, threshold condition. Three-level laser, properties of a laser beams, black-body radiation theory. Modes of a rectangular cavity, Raleigh-Jeans and Planck radiation formula. Semi-classical treatment of the interaction of radiation and matter.. Diffraction optics in paraxial approximation. Passive optical resonators, plane-parallel (Fabry-Perot) resonator, concentric, confocal, generalized spherical and ring resonator. Eigen-modes and Eigen-values. Stability condition, unstable resonator, photon lifetime and cavity Q. Q-switching, electro-optical, and acousto-optic Q-switches, saturable absorber Q-switch. Theory of mode-locking, active and passive mode-locking. Laser excitation techniques, optical, electrical, and chemical pumping, laser pumping, excitation transfer, meta-stable states and lifetimes. Types of lasers, solid-state, dye and semiconductor lasers, gas, chemical, free electron, and X-ray lasers, laser applications.

Computer technology and historical background, Basic principles and postulates of quantum mechanics: Quantum states, evolution, quantum measurement, superposition, quantization from bits to qubits, operator function, density matrix, Schrodinger equation, Schmidt decomposition, EPR and Bell’s inequality, Quantum Computation: Quantum Circuits, Single qubit operation, Controlled operations, Measurement, Universal quantum gates, Single qubit and CNOT gates, Breaking unbreakable codes: Code making, Trapdoor function, One time pad, RSA cryptography, Code breaking on classical and quantum computers, Schor’s algorithm, Quantum Cryptography: Uncertainty principle, Polarization and Spin basis, BB84, BB90, and Ekert protocols, Quantum cryptography with and without eavesdropping, Experimental realization, Quantum Search Algorithm.

Review of Quantum Mechanics and overview of Quantum information: Postulates of quantum mechanics, quantum states and observables, Dirac notation, projective measurements, density operator, pure and mixed states, entanglement, tensor products, no-cloning theorem, mixed states from pure states in a larger Hilbert space, Schmidt decomposition, generalized measurements, (CP maps, POVMs), qualitative overview of Quantum Information. Quantum Communication: Dense coding, teleportation, entanglement swapping, instantaneous transfer of information, quantum key distribution. Entanglement and its (search algorithm), modeling quantum measurements, Bekenstein bound, quantum error correction (general conditions, stabilizer codes, 3-qubit codes, relationship with Maxwell’s demon), fault tolerant quantum computation (overview). Physical Protocols for Quantum Information and Computation: Ion trap, optical lattices, NMR, quantum optics, cavity QED.

Second Order Differential Equations: Partial differential equations, Series solutions, a second solution, non-homogeneous equations, Green function. Sturm Liouville Theory: Self – Adjoint ODE’s, Hermitian Operators, Gram-Schmidt Orthoganalization. Laplace transforms and inverse Laplace transforms, Laplace transform of periodic functions. The convolution integral. Bessel Function: Bessel functions of first kind, Bessel function of 2nd kind, Neumann functions, Hankel functions. Legendre Functions: Generating function, recurrence relations, orthogonal, associated Legendre function, spherical Harmonics, applications to spheroidal coordinate system Special Functions: Hermite Functions, Laguerre Functions, Chebyshev polynomials, hypergeometric functions. Fourier Transforms: integral Transform Methods. Integral Equations: Integral equations integral transforms. Generating functions, Neumann series, Degenerate kernels, Hilbert-Schmidt theory. Nonlinear Differential Equations and its Solutions: Classification of nonlinear differential equation and its solutions.

Maxwell equations and Maxell’s displacement current, vector and scalar potential, Gauge Transforms, Lorentz and Coulomb gauge. Green’s function for conducting and non-conducting sphere, Greens function for wave equation, Retarded solutions for the fields, one dimensional Green’s function, two and three dimensional Green’s functions, Dirac Delta function, properties and uses. Poynting’s theorem and conservation laws, Poynting theorem in linear and dispersive medium, solution for harmonic fields, transformation properties of electromagnetic fields and sources—under rotation. Plane wave in a non-conducting medium, at the surface of and within a conductor, cylindrical cavities and wave guides, modes in a rectangular waveguides, energy flow and attenuation in waveguides. Power losses in a cavity and Q of a cavity, Schulman resonances, multimode propagation in optical fibers. Modes in a planer slab dielectric waveguides, modes in circular fibres, Fields in a hollow metallic wave guide.

Why Study Materials Science and Engineering? Classification of Materials (metals, ceramics, polymers, composites)). Properties (Mechanical, electrical and magnetic properties). Equilibrium and Kinetics (stable, unstable and metastable equilibrium). Review of thermodynamics terms (temperature, pressure, internal energy, enthalpy, etc.). Atomic Structure. Atomic Bonding in Solids. Bonding Forces and Energies. Primary Interatomic Bonds (ionic, covalent, metallic bonding).. Concept of diffraction in a periodic lattice. Structural information from x-ray diffraction and other diffraction techniques. Crystal structures of metals and ceramic materials. Point Defects. Vacancies and Self-Interstitials.. Diffusion Mechanism. Steady-State Diffusion Nonsteady-State Diffusion, Equilibrium diagrams having intermediate phases or compounds. Phase transformation: Basic concepts, Kinetics of phase transformations, Metastable versus stable transformations, Isothermal transformation diagrams, Continuous cooling transformation diagram.

Time evolution and Schrödinger equation, the Schrödinger versus the Heisenberg picture, interaction picture. Symmetries, conservation laws and degenerates. Discrete symmetries, Parity or space inversion, Lattice Translation as discrete symmetries Classical radiation field, Creation, annihilation and number operators, Quantization of radiation field. Relativistic Quantum Mechanics of Spin 1/2 particles, probability conservation in Relativistic quantum, the Dirac equation, Simple solutions, non-relativistic approximations, plane wave solutions Relativistic invariance of Dirac equation transformation properties of Dirac bilinear, adjoint Dirac equation, equation of continuity, constant of motion The Klein- Gordon Equation, Derivation and Covariance, Klein's Paradox and Zitterbewegung.

Quantum mechanics of continuous systems, discretization, infinite matrices, calculation of matrix elements between states characterized by continuous variables. Concept of classical paths, principle of least action, introduction to path integrals, propagator, simple harmonic oscillator in path integral representation. Adiabatic processes, Berry phase in atomic and molecular physics, quantum Hall effect, coherent states. Multiple vacua, tunneling phenomena, Supersymmetric quantum mechanics. Superconductivity and superfluidity: Meisner effect, Landau-Ginsburg theory, Cooper pairs. Basics of many body theory, particles and holes, RPA, Feynman diagrams for non-relativistic systems. Quantum theory of measurement, EPR paradox, Bell’s theorem, quantum logic, quantum computation.

Intensive and extensive quantities, thermodynamic variables, thermodynamic limit, thermodynamic transformations. Classical ideal gas, first law of thermodynamics, application to magnetic systems, heat and entropy, Carnot cycle. Second law of thermodynamics, absolute temperature, temperature as integrating factor, entropy of ideal gas. Conditions for equilibrium, equation of state, Fermi gas at low temperatures, application to electrons in solids and white dwarfs. The Bose gas: photons, phonons, Debye specific heat, Bose-Einstein condensation, equation of state, liquid helium. Canonical and grand canonical ensembles, partition function, connection with thermodynamics, fluctuations. minimization of free energy, photon fluctuations, pair creation. The order parameter, Broken symmetry, Ising spin model, Ginsburg – Landau theory, mean-field theory, critical exponents, fluctuation-dissipation theorem, correlation length, universality

When does size matter? Scales of Various Systems, Chemistry: atoms, molecules, clusters, Top Down approach, Bottom up approach, Chemical Approaches: Wet Chemical Synthesis of Nanomaterials, Sol gel process with examples.Gas phase synthesis of nanomaterials; Chemical vapor deposition (CVD), Furnace assisted synthesis, Gas Condensation Processing,Sputtered Plasma Processing: Microwave Plasma Processing, Particle precipitation aided Chemical Properties: reactivity and catalytic activity. Electronic and Optical properties: particle in a box, quantum-size-effect (QSE), quantum dots (Q-particles), quantum structures, and artificial atoms. Electrical Properties: size induced metal-insulator-transition (SIMIT), clusters of metals and semiconductors, and one-dimensional conductive nanowires. Mechanical Properties: nanostructured beams, and nanocomposites. Magnetic Properties: nano-scale magnets, transparent magnetic materials, and ultrahigh-density magnetic recording materials.

Band theory and electron correlations: Single electron in a periodic potential, many electrons in a periodic potential, Hartree-Fock-LDA and beyond. Fermi liquid theory and elementary excitations: Quasiparticles and Landau parameters, thermodynamics of a Fermi liquid. Second quantization: Second quantization for fermions and bosons, Quadratic Hamiltonians and canonical transformations. Quantization of lattice vibrations. Green’s functions: Green’s function and response functions, Dyson and Bethe-Salpeter equations, perturbation methods and Feynman diagrams, zero temperature versus ﬁnite temperature formulation. Fermi liquid theory: microscopic formulation: Landau quasiparticles as poles of Green’s function, Landau parameters, conservation law and Ward identities. Quantum magnetism: Spin waves, spin path integral, quantum non-linear sigma model. Modern applications: Kondo effect, quantum phase transitions, non-Fermi liquid.

Concepts of Helmholtz free energy and Gibbs free energy. Energy-property relationships, thermal equilibrium and chemical equilibrium. Gibbs-Helmholtz relationships. Equilibrium constant and its variation with temperature, vant Hoff’s equation. Clapeyron equation. Fugacity and chemical activity. ideal and regular solution models. Thermodynamics of solutions, Gibbs- Duhem relationship. Homogeneous and heterogeneous nucleation. The effect of temperature and pressure on phase transformation. Mixing functions. Excess functions. Thermodynamic properties and equilibrium phase diagrams. Phase Rule, Gibbs free energy and entropy calculations. Typical equilibrium Phase diagrams. Statistical mechanics/models in thermodynamics.

Introduction, importance of energy, world energy demand. Conventional energy sources, renewable sources; potential, availability and present status of renewable sources. Solar energy, physical principle of conversion of the solar radiation into heat, flat-plate collectors., biogas generation, classification of biogas plants. Geothermal sources, hydro-thermal geo- pressure, petro- thermal and magma resources, advantages and limitation of geo- thermal energy. Introduction, global generating on growth rate, prospects of nuclear fusion, safety and health hazards issues, global resources and their assessment. Classification, micro, mini, small and large resources. Principles of energy conversions, turbines, working and efficiency of from to small power systems, environmental impacts.

An introduction to solar energy, direct and in direct sources of solar energy. Review of semiconductor properties, materials and structural characteristics effecting cell performance. Short-circuit current limit, open-circuit voltage limits, effects of temperatures, short-circuit current losses, open-circuit voltage losses, fill factor losses, efficiency measurement.. Contribution to saturation current density, top-contact design, optical design, antireflection coating, textured surfaces, spectral response, silicon single crystal wafers for solar cells and modules, module construction, cell operating temperatures, module durability and circuit design. Advance materials for solar cell, pre and post surface modification of solar cells, polishing and chemical etching of basic photovoltaic materials. Annealing in various environments, ion-implantation, energy storage, power control and system sizing. Uses of solar cells in water pumping and residential systems, central power plants for space applications.

Introduction to symbolic computing (Matlab, Mathematica and Simulink), introduction to computers, errors estimation, methods for roots of nonlinear equations, linear system simulations (Gauss-elimination, Jacobi method, Gauss-Seidel method, LU decomposition), Eigen-value problems; Linear and nonlinear regressions, computational integration and differentiation, Ordinary Differential Equations (Euler method, Improved Euler method, KR-methods), Multi-step methods; Partial differential equations, introduction to Monte Carlo methods, Genetic Algorithms.

Introduction to mathematical modeling, fundamentals of simulation, Introduction to Matlab and Simulink, block model development in Simulink, first order models (examples from fluids, biophysics, physics, electrical systems and mechanical systems), second order systems and models (example on homogeneous and non-homogeneous linear systems coupled or simultaneous systems (examples from fluids and population, electrical and mechanical systems), nonlinear systems and simulation methods; stochastic models and simulation methods (discrete and continuous systems), probability density functions and sampling methods, random walks, introduction to MC techniques.

Crystal Structure, Atomic Bonding, Intrinsic and Extrinsic Semiconductors, Energy Bands, Density of States, Nearly Free Electron Model, Kronig-Penny Model, Energy Bands for Intrinsic and Extrinsic Semiconductors Fermi-Dirac Statistics, Carrier Concentrations in Thermal Equilibrium in Intrinsic Semiconductors and Semiconductors with Impurity Levels. Thermoelectric and Thermomagnetic Effects, Quantum Transport. Diffusion processes, Diffusion and Drift of Carriers, The Continuity Equation, Direct and Indirect Recombination of Electrons and Holes, Steady State Carrier Injection, Optical Absorption, Interband Transitions, Photoconductivity, Luminescence. Ohmic, Blocking and Neutral Metal-Semiconductor Contacts, PN-Junction under Equilibrium Conditions, Forward and Reverse-Biased Junctions, Reverse-Bias Breakdown, Deviations from the Simple Theory.

Magnetism & various magnetic materials with their applications, classical and quantum phenomenology of magnetism. orbital motion of a single electron, spin states of a single electron, states of isolated ions, ions in magnetic fields, spectroscopic investigations Quantum Mechanics, Magnetism and Bonding in Metals. Spontaneous magnetic order, ferromagnetisms in elements, ferromagnetism in alloys, ferromagnetism in non-metallic compounds, ferromagnetism & anti-ferromagnetism, linear and helical magnetism. magnetocrystalline anisotropy, shape anisotropy and stress anisotropy diamagnetism of isolated atoms and ions, diamagnetism of crystalline solids, diamagnetic resonance or cyclotron resonance, the main classes of paramagnetic solids, paramagnetism due to ions of rare-earth and transition elements, paramagnetism of metals, free radicals and molecular paramagnetism, paramagnetic relaxation. Soft Magnetic Materials theory and applications. Amorphous Materials: magnetism and disorder. Magnetism in Small Structures exchange coupling and nanocrystals.

Characterization of electromagnetic radiation, and its interaction with matter. Diffraction of x-ray and neutrons by crystalline material. Qualitative and quantitative analysis of the diffraction patterns. Energy dispersive and wavelength dispersive analysis, thermal analysis, Differential Calorimetric analysis. Thermal Gravimetric analysis (TGA). Molecular spectroscopy techniques, IR spectroscopy, UV-ViS spectroscopy, Transmission Electron Microscopy (TEM),( FTIR), gamma-ray spectroscopy, Mossbauer spectroscopy, Raman spectroscopy and Atomic Force Microscopy (AFM).Understanding of the data analysis qualitatively and quantitatively. Errors and Data Analysis: Errors of observation: accidental and systematic errors. Errors in compounds quantities, in products, in quotient in sum or difference. Frequency distributions and related terminology, methods of least squares, weighted mean and its standard error, curve fitting and accuracy of co-efficient.

The surface as an especially important object for physical investigation. Influece of the surface on physical properties of objects. Clean and covered surfaces. Adsorbtion and catalysis. What is UHV: Vacuum concepts and UHV hardware. The methods to get clean surfaces. The structure of surfaces. Short overview of modern experimental techniques. Lattice concept. 3 D crystal structures, 2D surface structures. Specific types of surface, fcc, hcp, bcc and stepped surfaces and a discussion of their relative energies. More complex to the theory and practice of SIMS, SIMS imaging and depth profiling, Auger depth profiling, theory and practice of Rutherford. Back scattering. Classification of microscopy techniques, Basic concepts in Surface imaging and localized spectroscopy, Imaging XPS, Optical microscopy, STEM. SEM.SPM. An introduction to the theory and practice of scanning Tunneling Microscopy, Scanning probe microscopy techniques, Atomic Force Microscopy.

Maxwell equations, dielectric optical response, refractive index and absorption, Lorentz oscillator model, dispersion relations, Lyddane-Sachs-Teller relation, Drude theory and basic plasma opticslight scattering, Raman and Brillouin scattering, coherent Raman spectroscopy. Direct and indirect gap semiconductors, energy and momentum conservation in band-to-band transitions, optical absorption and quantum mechanical time-dependent perturbation theory, dipole-allowed optical transition in the parabolic band approximation, indirect optical transitions, excitons, two-particle Schrodinger equation, selection rules, first-class dipole allowed transitions, second-class dipole allowed transitions, , excitons in quantum wells. Franz-Keldysh effect, DC Stark effect, exciton ionization, quantum-confined dc-Stark effect.Overview of Semiconductor Optical Nonlinearities: Phase-space blocking, screening, bandgap renormalization, thermal nonlinearities, optical Stark effect, two-photon absorption. Basic operation principles of LED's and lasers, doping p-n junctions forward and reverse bias, I-V curves, semiconductor lasers, photodetectors.

Basics of conducting polymers Synthesis, structures and morphology; Conductivity Properties: Semiconductor models and conductivity mechanisms in conducting polymers; Doping reactions: Composites, copolymers, conductive polymer thin films; Electrochromic and electrochemical properties of conducting polymers; Solubility and processing of conducting polymers; conducting polymer coatings, Characterization methods: Electrical, mechanical and electrochemical characterizations; Application fields of conducting polymers: Sensor applications, photovoltaic applications; supercapacitor applications, recent activities in the field of conducting polymers.

Introduction, Chemical bonding, Energies forces and bonds, Energy bands, Thermodynamics and statistical mechanics, Reaction rates, Transport processes, Biological polymers, Biological membranes, Biological energy, Movement of organisms, Excitable membranes, Nerve signals, Memory, Biological motors.

Principal layers, troposphere, stratosphere, mesosphere, thermosphere, Ideal gas model revisited,exponential variation of pressure with height, Escape velocity, Temperature structure and lapse rate. The Sun as the prime source of energy for the earth, Solar energy input, cycles daily and annual, Spectrum of solar radiation reaching the earth, Total radiation and the Stefan Boltzmann,. Thermodynamics of moist air and cloud formation, Growth of water droplets in clouds, Rain and thunderstorms. Measuring the wind; the Beaufort scale, Origin of winds; the atmosphere as a heat engine, The principal forces acting on an air parcel, Cyclones and anticyclones, Thermal gradients and winds, Global convection and global wind patterns. Design of buildings. Atmospheric pollution; acid rain: Systems approaches to environmental issues, Acid rain as a regional problem. Sound and noise: Definition of the decibel and A-weighted sound levels, Measures of noise levels; effect of noise levels on hearing, Domestic noise; design of partitions.

Early attempts at solar, declining costs of PV, Definition of Gen I, Gen II, and Gen III PV technologies, Solar resources planet-wide, Applications, Utility scale, "Distributed grid" rooftop applications, Current usage of solar PV. Capacity factor calculations, Comparison of solar PV to other Methods, Daily energy demand variations and peak usage, Energy storage methods and Costs, Differences in economic case for point of use PV versus utility scale power generation. Monocrystalline Si, Polycrystalline Si, Si thin film, CdTe and CIGS, High performance multijunction cells. Cell classification, Front side ribbon soldering, Cell interconnects and "stringing", Electrical circuit assembly, Laminate assembly, CPV. Power output, footprint, and cost: Effects of latitude and climate, Tracking Systems, Balance of system (inverters, mounting racks, installation costs). a-Si, CIGS, CdTe, Exotics. Discrete cell panels; Construction overview, Stringing, Layout, Wiring, Final Test. Thin Film Panels; Construction overview, Advantages over discrete, Fabrication techniques, Test. PQ standards & measurements, Case studies.

Models for radiation analysis and beam radiation calculations, evaluation and estimation of the solar resources. Thermal conversion of solar radiation, the concentration of solar radiation, overview of solar concentrating technology. Parabolic trough, paraboloidic dish: continuous type and Fresnel type. single axis and double axis trackings. Solar Parabolic trough; design considerations, tracking and control systems, thermal design of receivers. Solar parabolic dish; design considerations, Sterling engine, Brayton cycle, tracking and control systems. Solar tower concepts; tower design, heliostat design, receiver types, trackingand control systems. Material and product/technology overview for the above technologies. Linear Fresnel reflector, Solar chimney. Technology overview, design considerations, materials. Performance study, site selection and land requirement.

Current energy consumption, overview of biofuel/bioenergy and biorefinery concepts. Fundamental concepts in understanding biofuel/bioenergy production Renewable feedstocks and their production. Feedstocks availability, characterization and attributes for biofuel/bioenergy production Biomass preprocessing: drying, size reduction, and densification. Various biofuels/bioenergy from biomass. Biomass conversion to heat and power: thermal gasification of biomass, anaerobic Digestion. Biomass conversion to biofuel: thermochemical conversion, syngas Fermentation Biochemical conversion to ethanol: biomass pretreatment. Different enzymes, enzyme hydrolysis, and their applications in ethanol production Biodiesel production from oil seeds, waste oils and algae. Environmental impacts of biofuel production. Energy balance and life-cycle analysis of biofuel production. Value-added processing of biofuel residues and co-products.

Introduction to stochastic techniques, random number generation, probability theory, probability distribution functions, discrete and continuous pdfs, direct sampling methods, rejection techniques, importance sampling methods, random walks, diffusion and biased diffusion, Metropolis algorithm and its applications, error estimation and error reduction techniques, multivariate distributions, random walk filters, applications of MC methods (Ising model, Heisenberg model in statistical physics, neutron transport, radiation transport, study cases using large computer codes using MC methods such as GEANT-4, MCNP etc.

Dynamical systems, phase space, Poincare section, spectral analysis, Basin of attraction, bifurcation diagrams; the Logistic map, period doubling, Lyapunov exponents, entropy; Characterization of chaotic attractors; prediction of chaotic states, method of analogues, linear approximation method, modification of chaotic states; spatio-temporal chaos, intermittency; Quantum maps, chaos in non-equilibrium statistical mechanics, driven systems; inter-mode traces in the propagator for particle in the box.

Review of thermodynamics and Statistical Mechanics. Empirical equation of state. Ideal gas laws. Van der Waal’s equation. Critical Phenomenon. Hugoniot equation. Mie-Gruneisen equation. Semi-empirical theory of Gruneisen ratio. Theoretical calculations of equation of state. Exactly soluble models. Classical ideal gas. Non-interacting Fermi gas. Non-interacting Bose gas. Paramagnets. Ising model. Approximate methods. Thomson-Fermi model. Debye-Huckle theory. Statistical mechanics of Plasmas. Cluster expansions. Computer based calculations of equation of state. Methods of molecular dynamics and Monte Carlo Techniques.

Scattering theory, quantum scattering, calculation of cross-sections; Variational techniques, solution of generalized eigenvalue problems; Hartree-Fock method, the helium atom, many electron system, Slater determinants; Density functional theory, local approximation, exchange and correlation, applications; Molecular dynamics simulations, molecular systems, Langevin dynamics, ensembles and integrators, quantum molecular dynamics; Stochastic techniques; quantum Monte Carlo: variational diffusion, path-integral.

This is a course on advances in Physics not already covered in the syllabus. This special paper may be conducted as a lecture course or as an independent study course. The topic and contents of this paper must be approved by the BOS, AU.

This is a course on advances in Physics not already covered in the syllabus. This special paper may be conducted as a lecture course or as an independent study course. The topic and contents of this paper must be approved by the BOS, AU.

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