User talk:Chengappaiit

30.03.2010

1.Chemistry topics revision -NCERT papers. Chemistry-XI and XII 2.Physics-(Modern Physics ) 3.Gaussian Integrals.

31.03.2010

1. Lattice structures. 2. density of the structure of a lattice. 3. Inter atomic distances. 4. Solution for the hydrogen atom. 5. c/a for the hcc lattice structure.

01.04.2010

Structure of solids Thermodynamics and kinetics Solid-state physics. Inorganic and organic chemistry Basic quantum mechanics Semiconducting, dielectric, magnetic, optical, thermal and mechanical properties of solids Characterization of materials Basic mathematics

02.04.2010

Explain how you will use x-ray diffraction to determine the structure of solids? Draw the phase diagram of water and explain why the solid-liquid equilibrium has a negative slope? Explain the variation of free energy with particle size during homogenous nucleation? Explain the variation of specific heat of solids with temperature. How would you synthesize BaTiO3? What is the oxidation state of Cu in YBa2Cu3O7? Why is there a blue shift in the energy of light emitted with a reduction in size of nanoparticles? How does the Fermi level vary with doping? What crystal systems exhibit ferroelectricity? Why does one need a TEM and a SEM when the optical microscope is available? Plot y = A(1-e-x)

Basic Introductory Texts:

Introduction to Materials Science for Engineers, L. F. Shackelford, Pearson An Introduction to Materials Science and Engineering, Callister, Wiley Eastern Materials Science and Engineering, Raghavan, PHI Inorganic and Physical Chemistry, Phase transformations, Thermodynamics and Kinetics: Physical Chemistry, G. M. Barrow, Tata-McGraw Hill. Physical Chemistry of Metals, L. S. Darken and R. W. Gurry, CBS Publishers, Delhi. Inorganic Chemistry, D. F. Shriver and P. W. Atkins, OUP. Phase Transformations in Metals and Alloys, D. A. Porter and K. E. Easterling. Structure and Properties of solids: Solid State Chemistry and its applications, A. R. West, Wiley Eastern Edition Introduction to Solids, L. V. Azaroff, Tata McGraw Hill Introduction to Solid State Physics, C. Kittel, Wiley India edition Solid State Physics, N. W. Ashcroft and N. D. Mermin, Thompson/Brooks-Cole, Indian edition Solid State physics, A. J. Dekker, Macmillan India Limited Electrical Engineering Materials, A. J. Dekker, Prentice Hall of India. Electronic Engineering Materials and Devices, J. Allison, Tata McGraw Hill. Electrical Properties of Materials, L. Solymar and D. Walsh, OUP. Mechanical Metallurgy, G. E. Dieter, McGraw Hill Physical Metallurgy Principles, Reed-Hill, Thompson. Materials Characterization (The introductory texts also have sections on materials characterization): Elements of X-ray Diffraction, B. D. Cullity, Pearson Mathematics: Advanced Engineering Mathematics, E. Kreyzig, Wiley Eastern Edition.

03.04.2010

Application of principles of chemistry and physics to the properties of engineering materials. The relation of microstructure to mechanical, electrical, thermal and optical properties of metals. Solid material phase equilibria and transformations. The physical, chemical, mechanical and optical properties of ceramics, composites, and polymers. Operation and use of materials characterization instruments and methods.

04.04.2010 Prerequisite Skills:

Before entering the course the student should be able to: 1.	solve problems involving the concepts listed under course content; 2.	write short explanations describing various chemical phenomena studied; 3.	write balanced chemical equations including net ionic equations; 4.	write balanced chemical equations for oxidation-reduction reactions; 5.	describe the different models of the atom; 6.	use standard nomenclature and notation; 7.	calculate enthalpies of reaction using calorimetry, Hess's law, heats of formation and bond energies; 8.	describe hybridization, geometry and polarity for simple molecules; 9.	draw Lewis dot structures for molecules and polyatomic ions; 10.	describe the bonding in compounds and ions; 11.	describe simple molecular orbitals of homonuclear systems; 12.	predict deviations from ideal behavior in real gases; 13.	explain chemical and physical changes in terms of thermodynamics; 14.	describe the nature of solids, liquids, gases and phase changes; 15.	describe metallic bonding and semiconductors; 16.	define all concentration units for solutions and solve solution stoichiometry problems; 17.	collect and analyze scientific data, using statistical and graphical methods; 18.	perform volumetric analyses; 19.	use a barometer; 20.	use a visible spectrophotometer; 21.	perform gravimetric analysis. 22.	analyze engineering/science word problems to formulate a mathematical model of the problem; 23.	express in MATLAB notation: scalars, vectors, matrices; 24.	perform, using MATLAB or EXCEL, mathematical operations on vectors, scalars, and matrices a.	addition and subtraction b.	multiplication and addition c.	exponentiation; 25.	compute, using MATLAB or EXCEL, the numerical-value of standard mathematical functions a.	trigonometric functions b.	exponential functions c.	square-roots and absolute values 26.	import data to MATLAB for subsequent analysis from data-sources a.	data-acquisition-system data-files b.	spreadsheet files; 27.	construct graphical plots for mathematical-functions in two or three dimensions; 28.	formulate a fit to given data in terms of a mathematical curve, or model, based on linear, polynomial, power, or exponential functions a.	assess the goodness-of-fit for the mathematical model using regression analysis; 29.	apply MATLAB to find the numerical solution to systems of linear equations a.	uniquely determined b.	underdetermined c.	overdetermined; 30.	perform using MATLAB or EXCEL statistical analysis of experimental data to determine the mean, median, standard deviation, and other measures that characterize the nature of the data ; 31.	computer, for empirical or functional data, numerical definite-integrals and discrete-point derivatives 32.	solve numerically, using MATLAB, linear, second order, constant-coefficient, nonhomogenous ordinary differential equations; 33.	assess, symbolically, using MATLAB a.	the solution to transcendental equations b.	derivatives, antiderivatives, and integrals c.	solutions to ordinary differential equations; 34.	apply, using EXCEL, linear regression analysis to xy data-sets to determine for the best-fit line the: slope, intercept, and correlation-coefficient; 35.	draw using MATLAB or EXCEL two-dimensional Cartesian (xy) line-plots with multiple data-sets (multiple lines); 36.	draw using EXCEL qualitative-comparison charts such as Bar-Charts and Column-Charts in two or three dimensions; 37.	perform, using MATLAB and EXCEL, mathematical-logic operations 38.	compose EXCEL Visual-Basic MACRO programs/functions to automate repetitive spreadsheet tasks. 39.	analyze and solve a variety of problems often using calculus in topics such as: a.	addition, subtraction, dot product and cross product of vectors; b.	linear and rotational kinematics; c.	dynamics; d.	momentum; e.	work, kinetic energy, and potential energy; f.	rotational kinematics and dynamics; g.	statics; h.	gravitation; i.	fluids; j.	waves; 40.	operate standard laboratory equipment; 41.	analyze laboratory data; 42.	write comprehensive laboratory reports.

05.04.2010

1.	explain Atomic Structure and Interatomic Bonding 2.	compare and contrast crystal structure of solid materials 3.	explain solid imperfections, including both vacancy and self-interstitial crystalline defects 4.	apply the fundamental aspects of solid state diffusion as quantified by Fick's first and second laws in equation form 5.	evaluate the mechanical properties of metals using stress, strain, Poisson's ratio, elastic modulus, hardness, and ductility 6.	assess the effects of edge and screw dislocations to explain material-strengthening mechanisms 7.	Interpret the circumstances of material failure including: ductile/brittle fracture, fatigue cracking, and elevated temperature creep 8.	examine, appraise, draw/sketch, and explain phase diagrams 9.	Use phase diagrams to determine phase compositions and mass-fractions 10.	examine, appraise, draw/sketch, and explain phase transformations in metals 11.	describe the applications and processing of metal alloys including ferrous and nonferrous alloys 12.	compare and contrast the structures and properties of ceramics 13.	describe the applications and processing of ceramics 14.	compare and contrast polymer structures 15.	explain the major characteristics, applications, and processing of polymers 16.	compare and contrast the structures and properties of composite materials 17.	explain the major characteristics, applications, and processing of Composite Materials 18.	identify and assess the electrical and electronic properties of solid materials 19.	identify and assess thermal properties of solid materials 20.	identify and assess the magnetic properties of solid materials 21.	identify and assess the optical properties of solids 22.	operate materials characterization laboratory equipment, including: a.	hardness (Rockwell and/or Brinell) hardness tester b.	tensile strength tester c.	metallurgical microscope d.	scales, dividers, calipers, micrometers e.	grinders/polishers f.	digital multimeter (DMM) g.	precision weight scales 23.	function with increased independence in laboratory: set-up and perform the experiments based on the instructions in the laboratory sheets, and to analyze laboratory data and present experimental using MATLAB, all without extensive input on the part of the instructor.

06.04.2010

1.	Introduction of Materials Engineering a.	classification of materials b.	advanced materials such as carbon composites, liquid metals, superconductors 2.	Atomic structure and interatomic bonding a.	atom models; electrons in atoms b.	periodic table and electronic structure c.	interatomic bonding: types, forces, energy d.	molecule formation and structure 3.	Crystal structure a.	crystal unit cells b.	metal crystal structures c.	density calculations d.	crystal systems 1)	coordination number 2)	atomic packing factor e.	crystallographic points, directions, planes, miller indices f.	crystalline and noncrystalline materials 3)	single crystal 4)	polycrystal 5)	amorphous 4.	Solid imperfections a.	point defects 1)	vacancies and interstitials 2)	impurities b.	defect density as a function of temperature c.	line-defects and dislocations d.	bulk defects e.	microscopic examination techniques/methods 5.	Solid State diffusion a.	diffusion mechanisms and driving force b.	diffusion coefficient as function of temperature c.	fick’s first and second laws d.	steady-state diffusion e.	transient diffusion f.	steady-state diffusion calculations g.	factors that influence diffusion h.	numerical analysis using MATLAB 6.	Mechanical properties of metals a.	engineering/true stress and strain definitions and calculation b.	elastic and shear modulus of elasticity c.	poisson’s ratio d.	elastic deformation 1)	stress-strain behavior 2)	elastic properties of materials e.	plastic deformation 1)	true stress-strain behavior 2)	elastic recovery 3)	compressive, shear, and torsional deformation f.	hardness g.	variability of materials properties; factor of safety h.	numerical analysis using matlab 7.	Dislocations and strengthening mechanisms a.	characteristics of dislocations and dislocation-movement b.	slip systems c.	resolved shear stress and critical resolved shear stress d.	grain size strengthening e.	solid-solution strengthening f.	strain hardening and cold work g.	recovery, recrystallization, and grain growth 8.	Mechanical failure a.	ductile/brittle fracture b.	linear elastic fracture mechanics, and crack growth/propagation c.	impact testing d.	mechanical fatigue 1)	cyclic stresses 2)	s-n curve 3)	crack propagation 4)	factors affecting fatigue performance e.	elevated temperature creep 1)	three phase creep 2)	stress and temperature effects 3)	creep resistant alloys 9.	Phase diagrams a.	solubility limit b.	phases c.	microstructure d.	phase equilibria e.	equilibrium phase diagrams 1)	phase proportions by the lever law 2)	eutectic: systems, alloys, reactions f.	iron-carbon phase diagram 1)	fe-fec phase diagram 2)	iron-carbon alloy microstructure development 3)	alloying elements 10.	Solid phase transformations a.	phase transformation kinetics: nucleation and growth b.	multiphase transformation c.	isothermal phase transformation diagrams d.	continuous cooling transformation diagrams e.	in the Fe-FeC system formation of: austenite, pearlite, martinsite, bainite, spherodite f.	mechanical behavior of Fe-FeC alloys – strength vs. microstructure 11.	Applications and processing of metal alloys a.	ferrous and nonferrous alloys b.	cast-irons, steels, stainless steels c.	forming and casting d.	post process heat treatment e.	precipitation hardening 12.	Ceramics a.	crystal structures; anion-cation, b.	electroneutrality and stoiciometry c.	imperfections d.	diffusion in ionic materials e.	phase diagrams f.	fracture mechanics g.	stress-strain behavior 13.	Applications and processing of ceramics a.	Glasses – composition and processing b.	clay products c.	refractories d.	portland cements e.	advanced ceramics f.	temperature effects – glass transition temperature 14.	Polymer structures a.	hydrocarbon molecules b.	polymer molecules and chemistry c.	molecular: weight, structure, shape, configuration d.	thermoplasts and thermosets e.	polymer crystals f.	polymer defects 15.	Characteristics, applications and processing of polymerss a.	Stress Strain behavior 1)	strain-rate effects 2)	relaxation modulus b.	deformation mechanisms c.	temperature effects 1)	melting and glass transition temperatures strain-rate effects 2)	leathery, rubbery, and viscous-flow regimes d.	heat treatment e.	vulcanization f.	fabrication methods 16.	Solid composites a.	primary constituents: matrix, dispersed-phase b.	particle reinforced – large and small c.	fiber reinforced - continuous and discontinuous d.	structural 17.	Electrical/Electronic properties of materials a.	ohm’s law b.	electrical conduction c.	energy band structure d.	metallic conduction – affects of alloying e.	intrinsic/extrinsic semiconductors f.	doping and semiconduction – free charge density, and charge mobility, temperature effects g.	semiconductor devices – 3)	p/n junctions 4)	Transistors: MOSFET, BJT h.	dielectric behavior and capacitance 18.	Thermal properties of materials a.	Specific heat, coefficient of thermal expansion, thermal conductivity b.	Thermal stress c.	Thermal Shock 19.	Magnetic properties of materials a.	solenoid physics b.	flux density, magnetization, permeability, susceptibility c.	diamagnetism and paramagnetism d.	ferromagnetism and antiferromagnetism e.	curie temperature f.	domains and hysteresis g.	soft and hard magnetic materials 20.	Optical properties of materials a.	electromagnetic radiation – spectrum and propagation b.	photons and EM waves c.	light interactions with solids d.	refraction e.	reflection, absorption, transmission f.	material color g.	luminescence h.	photoconduction 21.	Laboratory exercises on materials characterization a.	determination of pure-metal and alloy-metal electrical resistivity; comparison to published values b.	microscale feature measurement using the metallurgical microscope c.	Rockwell hardness testing for round and flat metal specimens; comparison to published values d.	Brinell hardness testing for flat metal specimens; comparison to published values e.	tensile testing to fracture for ferrous, nonferrous, and plastic materials 1)	determine yield and ultimate strength; comparison to published values 2)	determine modulus of elasticity; comparison to published values f.	laminated, sandwich-composite beam deflection: 1)	sandwich-core 2)	one-sided sandwich 3)	two-sided sandwichoscilloscope 4)	determine the effective modulus of elasticity for the composite structure g.	use of standard engineering-lab tools 1)	calipers and micrometers 2)	digital multimeter 3)	metallurical microscope 4)	grinders & polishers 5)	personal-protective safety equipment

Methods of Presentation:

1.	Formal lectures using PowerPoint and/or WhiteBoard presentations 2.	Laboratory demonstrations 3.	Computer demonstrations 4.	Class discussion of problems, solutions and student’s questions

Assignments and Methods of Evaluating Student Progress:

1.	Typical Assignments a.	Read chapter-3 in the text on the structure of crystalline structure of materials b.	Exercises from the text book, or those created by the instructor 1)	Derive planar density expressions for the BCC (100) and (110) planes in terms of the atomic radius, R. 2)	Consider copper diffusion in nickel. At what temperature will the diffusion coefficient for have a value of 6.5x10-17 m2/s? Use the diffusion data in textbook table 5.2 3)	Explain why FINE PEARLITE is harder and stronger than COARSE PEARLITE, which in turn is harder and stronger than SPHERODITE 4)	The diagram at right contains the B-H curve for a steel alloy. Given this curve, determine the: a)	Saturation flux density b)	Saturation magnetization c)	Remanence d)	Coercivity

Mathematics

Space curves arc length tangent normal space binormal curvature curves surfaces tangent surfaces involute evolute intrinsic equations helices curves on surfaces surface of revolution helicoids matrices & direction coefficients families of curves isometric correspondance geodesics canonical geodesic equations normal property of geodesics existance theorems geodesic parallels geodesic curvature surface of constant curvature conformal mapping principle curvature line of curvature devolapables associated with space curves curves on a surface minimal surfaces ruled surfaces fundamental equations of surface parallel theory of surfaces general solution for homogeneous differential equation use of known result to find unknown the homogeneous equation with constant coefficients method of undetermined coefficients variation of parameters vibration in mechanical systems newton's law of gravitation and the motion of planets power series and their solutions ordianary points regular singular points gauss hypergeometric equations the point at infinity Legendre polynomials Properties of legendre polynomials Bassel's functions Gamma functions Group theory Normal sub groups Quotient groups homomorphisms automorphisms cayley's theorem Permutation groups Counting principles Sylow's theorem Rings Ideals Quotient rings Integral domains Eucleadian rings polynomial rings polynomials over rational fields and commutative rings vector spaces and modules dual spaces extension fields roots of polynomials elements of Galois theory Solvability by radicals Galois group over the rationals Algebra of linear transformations Characteristic roots Matrices and their forms Traingular form Canonical form Jordan form Nilpotent transformations Hermitian transformations

Unitary transformations Normal transformations Real quadratic forms Finite fields Wedderburn's theorem Finite division rings Darivatives and continuity algebra of derivatives Functions with non zero derivatives Rolle's theorem Mean value theorem Taylor's formula with remainder properties with monotonic functions functions of bounded variation The Reimann-Steltjes integral Sequences of functions Measure theory Lebesgue integral infinite product gamma functions tests of convergence Rearrangement of factors in product Tennery theotem Hyperbolic function Bernouli's numbers

Physics

Review of Newtonian mechanics, inertial frames of reference; Galilean Principle of Relativity; non-inertial frames. Generalised co-ordinates, the Principal of Least Action, the Lagrangian. Motion in one dimension and turning points - relation between the potential energy and the period of motion. The two-body central force problem, Kepler motion. Small oscillations, normal modes, forced and damped oscillations under friction- non-linear oscillators, perturbation theory and parametric resonance, motion in a rapidly oscillating field. Rigid body motion- Euler’s angles and equation - the asymmetric top. Collision theory - scattering, small angle scattering, Rutherford’s formula. Hamiltonian formulation, canonical transformations, Poisson brackets. Liouville’s theorem Hamiltonian-Jacobi theory, Action-Angle variables. Phase space, phase space trajectories, fixed points and their stabilities. Vector analysis, Green, Gauss and Stokes theorems. Linear vector spaces and linear operators. Matrices & eigenvalue problem. Theory of complex variables, Cauchy-Riemann conditions, Cauchy integral theorem, Taylor- Laurent expansion, classification of singularities, analytic continuation, theorem of residues and evaluation of definite integrals and series. Ordinary differential equations and series solution. Sturm-Liouville problem and orthogonal functions, special functions. Green’s functions for self-adjoint differential operators and eigenfunction expansion. (Laplace, Poisson, Diffusion, Wave equation etc to be discussed). Need for Quantum Mechanics. Operators and Linear Vector Spaces to describe observables and states of a system. Eigenstates and eigenvalues. Expansion into eigenstates and probabilistic interpretation. Canonical commutation relations. Uncertainty principle. Position and momentum representations. Wavefunctions. Schr¨odinger and Heisenberg equations of motion. Probability density and probability current densities. Ehrenfest Theorem. Stationary states; Non-stationary states: as examples Gaussian and Airy wave-packets for a free particle. Time-independent Schr¨odinger equation. One dimensional problems: bound states, reflection and transmission, linear harmonic oscillator, the coherent state, tunnelling through potential barriers and examples. Illustrations from mesoscopic physics, quantum wires etc Motion in three dimensions. Central potential problems (bound states in 3D). Symmetry in quantum mechanics. Angular momentum and spin; Addition of angular momenta. Electrostatics & methods of solving boundary value problems, Multipole expansion of electrostatic potentials. Dielectrics. Biot-Savart Law & Ampere’s Law. Vector potential. Faraday’s Law and time-varying fields. Maxwell’s equations, energy and momentum of the electromagnetic field, Poynting Vector, Conservation Laws. Introduction to Fortran programming and basic numerical methods will be imparted to the students through lectures and projects based on the numerical analysis of elementary physical problems illustrating such techniques. Review of thermodynamics. Need for statistical mechanics. Basic ideas of probability and statistics, random walks, Gaussian and Poisson Distributions, Central Limit Theorem. Distribution functions and phase space. Liouville equation, mixing and ergodicity. Ensembles: Micro canonical, Canonical, Grand canonical. Partition function - connection with thermodynamic potentials Quantum Ideal Gases - Fermi-Dirac/Bose-Einstein Statistics. Various applications of ideal fermions to specific heat and susceptibility of metals, etc. Various applications of ideal bosons to black body radiation and Planck distribution, etc. Imperfect gases. Basic ideas of phase transitions. Elements of Group Theory. Fourier and Laplace transforms, Saddle point method and asymptotic expansions. Integral Equations Calculus of Variations. Functional integration and functional differentiation. Scattering theory - Born approximation and partial wave analysis. Time independent perturbation theory. Variational method The WKB approximation. Time independent perturbation theory (Fermi’s Golden Rule). Adiabatic and Sudden Approximations Geometric Phases and the Bohm-Aharanov Effect. Rotation group, Tensor operators and the Wigner-Eckart theorem. Illustrations from atomic, molecular and nuclear physics. Pure and Mixed states. Density Matrix formalism Lorents Invariance of Maxwell’s equations; Review of Special Relativity; Maxwell’s equations in covariant form; four-vector potential and the electromagentic field tensor. Propagation of plane electromagnetic waves, reflection and refraction. Propagation through anisotropic and chiral media. Radiation from an accelerated charge, retarded and advanced potentials. Radiation multipoles Wave guides, Resonant Cavities. Error analysis: Errors in observation and treatment of experimental data, estimation of error, theory of errors and distribution laws, least squares method, curve fitting, statistical assessment of goodness of fit. 2. Basic measurement techniques and the underlying physical principles • Low temperature • Low voltage • High vacuum 3. Spectroscopic techniques: Theory and experiments 4. Theory and experiments in Nanophysics Path Integral Formulation of Quantum Mechanics. Relativistic quantum mechanics : Klein-Gordon and Dirac equations. Relativistic hydrogen atom. Canonical quantization of fields : the Schr¨odinger field and its applications to many-body problems. (Illustration through superfluidity, superconductivity, hard-sphere bose gas etc.) Quantization of real and complex scalar fields, and the Maxwell field (non-covariant quantisation in the radiation gauge). Spontaneous and Induced Emission of Photon from Atoms. Covariant perturbation theory. QED at tree level and calculation of processes such a Compton scattering, Moller scattering, etc. Binding and cohesion in solids. Bonds and bands. Crystal Structure, X-ray Diffraction, Reciprocal Lattice. Periodic potentials, Bloch’s Theorem, Kroning Penney Model, Free electrons and nearly free electrons; tight binding approximation. Elementary ideas of band structure of crystalline solids. Concept of holes and effective mass; density of states; Fermi surface; explanation of electronic behaviour of metals, semi-conductors and insulators. Lattice vibrations, harmonic approximation, dispersion relations and normal modes, quantization of lattice vibrations and phonons. thermal expansion and need for anharmonicity. Transport properties of solids. Boltzmann transport equation. Wiedemann-Franz law. Hall effect. Superconductivity: Phenomenology, penetration depth, flux quantization etc. Josephson effect. Semiconductors: intrinsic and extrinsic, carrier mobility etc. Thermal properties of solids. Magnetism in solids. Accelerators Passage of Radiation through matter Detectors The nuclear two-body problem The Liquid Drop Model. The Shell Model. The Collective Model. Beta decay of nuclei. Gamma decay of nuclei. Relativistic notations. SU(2) and the rotation group. Lorentz Group and SL(2,C). Homogeneous and Inhomogeneous Lorentz Group and their Algebras. Spinors. Relativistic Covariant Equations- Klein Gordon, Dirac and Maxwell equations. Quantization of free fields: Canonical and Path Integral Approach. Covariant quantisation of the Maxwell field. Interacting Fields and the Gauge Principle. Feynman-Dyson Perturbation Expansion and Feynman Diagrams. Quantum Electro-Dynamics. Tree Level Calculations of Compton Scattering Cross-section etc. Loops, Divergences, Regularization and Renormalization. Anomalous magnetic moment of the electron and the Lamb-Shift. Special theory of relativity. Tensor analysis. Covariant and contravariant tensors. Metric tensor. Affine connection and curvature tensor. Bianchi identities. General theory of relativity. Equivalence principle. Principle of general covariance. Geodesics and equation of motion of particles. Gravitational field equations. Schwarzschild solution. An introduction to the standard big-bang cosmological model. Cosmological principle. Robertson-Walker metric. Hubble’s law and red-shifting of light. Energy-momentum tensor for a perfect fluid. Equation of state and solution of Einstein’s equations for radiation, matter and vacuum energy. Cosmic microwave background radiation. Review of perturbation theory for time evolution operator (propagator) - interaction picture Time evolution in frequency (Fourier-Laplace transform domain) - resolvent expansion - Lippman-Schwinger equation - T matrix/multiple scattering theory. Finite temperature Green’s function - retarded case - application to superconductivity. Salpeter equation. Ward identitites and Feynman diagrams. Ring and ladder diagrams - Bethe-Bruckner-Goldstone theory. Coulomb interaction - Hartree-Fock theory - Random Phase Approximation (RPA). Electron-phonon (Frohlich) interaction - superconductivity. Superfluidity. Quantum Chemistry and the Nature of the Chemical Bond. Chemical Kinetics and Thermodynamics. Order of the Reaction. Rate laws. Mechanism of Chemical Reactions: (a) Collision Theory (b) Transition State Theory (c) Potential Energy Surface (d) Kramers Escape Rate. Enzyme Reactions: Solution kinetics, characterization of enzymes, control mechanisms. Electron Transfer: (a) Dynamical Electrochemistry (b) Electron Transfer (c) Quantum Models (d) Electron Charge Transfer in Proteins. Plasma State of Matter: Introduction Motion of a charged particle in electromagnetic field. Plasma as a fluid; elementary discussions on wave motion in plasma. Fluid nature of plasma, waves in a ”cold” plasma. Derivation of the general dispersion relation, different types of waves in plasma and their classification. Dispersion relations for different waves, Effects of finite temperature on wave propagation. Kinetic theory of Plasma. Elements of Magneto-hydrodynamics (MHD) Elements of Parametric excitation and nonlinear waves in Plasma. Experimental methods for measuring plasma parameters. Elementary ideas of confinement of high temperature plasma. Books Goldstein : Classical Mechanics Landau and Lifshitz : Mechanics Percival and Richards : Classical Dynamics Marion : Mechanics Hand and Finch, Analytical Mechanics. G. Arfken, Mathematical Methods for Physicists I.N. Sneddon, Special Functions of Mathematical Physics & Chemistry P.K. Chattopadhyay, Mathematical Physics E. Kreyszig, Advanced Engineering Mathematics Mathews and Walker, Mathematical Physics P. Dennery & A. Kryzwicki, Mathematics for Physicists C.M. Bender & S.A. Orszag, Advanced Mathematical Methods for Scientists & Engineers E. Butkov, Mathematical Physics R.W. Churchill & J.W. Brown, Complex Variables & Applications Merszbacher : Quantum Mechanics Sakurai : Modern Quantum Mechanics Cohen-Tannoudji, Diu and Lal¨oe, Quantum Mechanics I Schiff : Quantum Mechanics Landau and Lifshitz : Quantum Mechanics Messiah : Quantum Mechanics I and II Powell and Craseman : Quantum Mechanics K. Gottfried, Quantum Mechanics Bransden and Joachim, Introduction to Quantum Mechanics Townsend, Quantum Mechanics J.D. Jackson, Classical Electrodynamics J.R. Reitz, F.J. Milford & R.W. Christy, Foundations of Electromagnetic Theory. D.J. Griffiths, Introduction to Electrodynamics Price, Analog Electronics (Prentice-Hall) Hickman, Analog Electronics (Newnes) Bogart, Electronic Devices and Circuits (Universal Book Stall) Streetman, Solid State Electronic Devices (P/H/I) Horowitz and Hall, The Art of Electronics (Cambridge) Callan, Introduction to Thermodynamics & Thermostatistics F. Reif, Fundamentals of Statistical & Thermal Physics R.K. Pathria, Statistical Mechanics L.E. Reichl, A Modern Course in Statistical Physics Kerson Huang, Statistical Mechanics Landau & Lifshitz: Quantum Mechanics Messiah, Quantum Mechanics I & II Davidov, Quantum Mechanics Sakurai : Modern Quantum Mechanics Cohen-Tannoudji, Diu & Lal¨oe, Quantum Mechanics II Ryder, Quantum Field Theory Flugge, Practical Quantum Mechanics J.D. Jackson, Classical Electrodynamics J.R. Reitz, F.J. Milford & R.W. Christy, Foundations of Electromagnetic Theory. Dekker, Solid State Physics Kittel, Introduction to Solid State Physics Ashcroft and Mermin, Introduction to Solid State Physics. Ziman, Principles of the Theory of Solids. Subatomic Physics, H. Frauenfelder and E.M. Henley, Prentice Hall 1974. W.E. Burcham and M. Jobes, Nuclear and Particle Physics, Addison Wesley 1998 Pooh, Rith, Scholz and Zetsche, Particles and Nuclei, Springer 1995. D.H. Perkins, Elementary Particle Physics A. Preston & A. Bhaduri, Nuclear Physics S. Weinberg, Gravitation and Cosmology Misner, Thorne and Wheeler, Gravitation R. Wald, General Relativity. Kolb and Turner, Early Universe. A. L. Fetter and J. D. Walecka, Quantum Theory of Many Particle Systems G. D. Mahan, Many Particle Physics Mattuck, A Guide to Feynman Diagrams in the Many Body Problem Negele, P. Nozieres and D. Pines, The Theory of Quantum Liquids, Vols. I & II Principles of Plasma Physics, N. A. Krall and A. W. Trivelpiece, McGraw-Hill (1973) Introduction to Plasma Theory, D. W. Nicholson, John Wiley (1983) Introduction to Plasma Physics (2nd Ed), F. F. Chen, Plenum Press (1989) Plasma Physics - Basic theory with fusion application, (2nd Ed.) K. Nishikawa and M. Wakatani, Springer-Verlag (1994) Fundamentals of Plasma Physics (2nd Ed.), J. A. Bittencourt, (Published by Bittencourt (1995)) The Physics of Fluids and Plasmas, An Introduction for Astro Physicists, Arnab Raichaudhuri, Cambridge Univ. Press, First South Asian Ed. (1999) Chaikin & Lubensky, Principles of Condensed Matter Physics Hansen & Mcdonald, Theory of Simple Liquids De Gennes, Liquid Crystals Landau & Lifshitz, Theory of Elasticity Doi & Edwards, Polymers De Gennes, Scaling Concepts in Polymer Physics Solids Far From Equilibrium, ed. C. Godriche Baraban & Stanley, Fractal Properties of Surface Growth Debashish Chowdhury, Physics Reports. P. Bak, How Nature Works. A. Mehta, J. Preskill, http://www.theory.caltech.edu/people/preskill/ph229 A. Peres, Quantum Theory: Concepts and Methods. Electronic Structure of Solids and Alloys, eds. O.K. Andersen, V. Kumar, A. Mookerjee. (World Scientific) - Electronic Structure of Solids, O.K. Andersen, O. Jepsen (Proceedings of the Varenna School, 1983) - SERC School Lecture Notes, 2000, Calcutta : S.K. Ghosh, M. Harbola Phase Transformations, Ducastelle and Gautier Theory of Phase Transformations, Khatchaturyan, Rev. Mat.Science Spin Glasses, D. Chowdhury and A. Mookerjee, Physics Reports Spin Glasses, D. Chowdhury (World Scientific)

Physical Properties Chemical properties Thermal properties Mechanical properties Optical properties Magnetic properties absorption Reactivity against other chemical substances Thermal conductivity Young's modulus Permeability

albedo Heat of combustion Thermal diffusivity Specific modulus Absorptivity Hysteresis

area Enthalpy of formation Thermal expansion Tensile strength Reflectivity Curie Point

brittleness Toxicity	Seebeck coefficient Compressive strength Refractive index boiling point Chemical stability in a given environment Emissivity Shear strength Color capacitance Flammability Coefficient of thermal expansion Yield strength Photosensitivity color Preferred oxidation state(s) Specific heat Ductility Transmittance concentration Coordination number Heat of vaporization Poisson's ratio conductance Capability to undergo a certain set of transformations, for example molecular dissociation, chemical combination, redox reactions under certain physical conditions in the presence of another chemical substance	Heat of fusion Specific weight density Preferred types of bonds to form, for example metallic, ionic, covalent Pyrophoricity dielectric pH Flammability ductility Hygroscopy Vapor Pressure distribution Surface energy Phase diagram efficacy Surface tension Binary phase diagram electric charge Specific internal surface area Autoignition temperature electric field Reactivity Inversion temperature electric potential Corrosion resistance Critical temperature emission Glass transition temperature flow rate Eutectic point fluidity Melting point frequency Vicat softening point impedance Boiling point inductance Triple point intensity Flash point irradiance Curie point length location luminance luster malleability magnetic field magnetic flux mass melting point moment momentum permeability permittivity pressure radiance solubility specific heat resistance reflectivity spin strength temperature tension thermal transfer velocity viscosity volume

________________________________________ The Michelson Interferometer ________________________________________

History: ________________________________________  Back in the early days, the only waves that people could observe were those travelling in some sort of medium. For example, the waves in a river or the ocean were seen travelling in water. Therefore, there natural conclusion to be made by many people (Most importantly Huygen) that light, if it were to be a wave, and it had been proven to exhibit characteristics of them, would have to be travelling in some medium. As history would dictate, this mysterious medium that nobody could perceive with their senses or instrument, would be deemed the "luminiferous ether". Light, as well as all of the solar systems in the universe were said to be ensconced in this ether which would have to maintain a wave speed of 3e8 m/s (according to Maxwell's predictions at the time). The team of the two professors,  Michelson and Morley, would attempt to detect the presence of the elusive ether in 1880. To do so, they devised the interferometer which would allow them to observe the effect of the motion of the medium upon the propagation of light. Hence, interferometry was born around the famous "null outcome" experiment performed by Michelson and Morley in the late nineteenth century.

________________________________________ Theory of the Michelson Interferometer: ________________________________________   The picture below represents an interferometer in its simplest form: A source S emits monochromatic light that hits the surface M at point C. M is partially reflective, so one beam is transmitted through to point B while one is reflected in the direction of A.  Both beams recombine at point C to produce an interference pattern (assuming proper alignment) visible to the observer at point E.  To the observer at point E, the effects observed would be the same as those produced by placing surfaces A and B' (the image of B on the surface M) on top of each other. Let's look at this interaction in more detail. Imagine that we two surfaces M1 and M2 as diagramed below: The light of interest originates at point S until it comes into contact with the two surfaces (we assume the angles of incidence are the same) and is reflected to point P. Here theta is the angle of incidence for the light, t represents the separation of the two surfaces, and phi is the angle between them which can be assumed small enough to ignore. The difference in paths of the two beams, delta, originating at S can then be described by. If we make the intersection of the planes M1 and M2 be vertical, the distance between the mirrors to P is d, and the angle between the normal to M1 i, then the above expression can be written as  (assuming i is small). Now one can write an expression for the phase difference for the light, alpha,. This equation, however, presents quite a wide range of values for the phase which might make it impossible, or at least very hard to observe interference phenomena because we want the phase difference to be small (see my explanation why in the discourse on light basics). Therefore, delta must be for a particular change in the angle of incidence, theta. This modification can be done by taking the derivative of delta with respect to theta and setting it equal to zero. In doing so, we find that the different parts of the interference pattern can't be seen unless the distance between the two planes M1 and M2, t0 ,is zero when d=0 (case where interference effects are localized at M1 and M2), or if the angle between the two plane surfaces is zero and P=infinity. Intuitively, this makes sense because the smaller the distance between the two planes, the smaller the distance for the phases of the two rays to get less uniform. From this situation, it also becomes possible to determine the shape of the interference effects. As it turns out, the effects are either linear or circular patterns. Lets redraw the coordinate above to see mathematically how to obtain these fringe patterns (i.e. the situation pictured below). One now looks at the two planes from the front instead of the side. The observer resides at point O, R is the base of the perpendicular from O onto the plane M1, and the ray OR=z. The path difference, as we have proved above, from M1 to M2 is. The ray OP is the hypotenuse of the triangle OPR so it is equal to. The cosine of the angle theta, which will be important in a moment, can then be expressed as. The surface thickness at point R will be designated "e", so at the point P(x,y)  the thickness is defined to be , where alpha is the angle that separates the two planes (It was phi in the diagram above it). For stationary waves, the normal modes occur at integer multiples of the lights' wavelength given by the following formula. If we had a wave on a string, L would the length of the string itself. In our case, however, it is the distance from the plane M2 to the plane M1. Thus, this distance. Now we can write an expression that governs the behavior of the fringes that we see at point O. This relationship is. Consider the two important cases that determine the shape of the interference patterns observed at point O. The first case occurs when both M1 and M2 intersect at the perpendicular, point R.  Here the thickness of the surfaces, e, is zero. Thus, the  fringe determining equation is rearranged to. The relationship was able to be reduced by making the assumption that z >>x+y and alpha is small. The resulting expression is that of a line with fringes separated by distance. Interestingly enough, if the observer is too close to the surface planes M1 and M2, this assumption can't be made. The result is a hyperbolic function causing the fringes to appear slightly bent. The second case to be considered appears when the two surface planes are parallel to each other (i.e. the angle alpha between them is zero). Thus,our fringe governing equation gets rearranged yet another time to yield: Clearly this represents the equation of a circle, hence our fringes appear circular to the observer. One more important point to remember is the property of coherence length when it comes to a device that studies interference effects. If the differences in path length to both the mirrors and back from the beamsplitter is greater than the coherence length, then no interference effects will be seen. Thus, when adjusting the moveable mirror on the Michelson interferometer, one must be precise when trying to find interference patterns of light comprised of a large difference in wavelengths, such as white light. Now that you understand how we get these fringes, lets see if we can reproduce them with a Michelson Interferometer! ________________________________________ Studying the Wave Nature of Light with a Michelson Interferometer: ________________________________________   The Michelson Interferometer represents a device that takes advantage of the Wave Nature of Light. If light were not to be considered a wave, none of the observed interference patterns could occur in experiments as they do. In this section, how light can interact and interfere with itself to produce these fringes and patterns characteristic those of waves is described. Below (thanks to my partner on the project that we performed this semester, Seth Carpenter) we see an interferometer a little more complex than that used in the theory discussion. The main difference between the one used to derive theory and the one picture above, is the addition of the "compensatory lens". This lens is added so that both paths, from the back of beam splitter to Mirror 1 and Mirror 2, are identical. This addition becomes necessary since the back of the beam splitter is where the light gets reflected (usually by a partially reflective silver coating). Thus, the light travelling to Mirror 1 travels through the thickness of the beamsplitter 3 times; once as it enters initially, next as it is reflected off the back of it, and finally as it returns to the beamsplitter after reflecting off of Mirror 1. If the compensatory lens were not in place, the light travelling to Mirror 2 would only travel through the beamsplitter once since it is transmitted through it and then reflected off the back of it. Therefore, the compensatory lens MUST be of exactly the same thickness as the beam splitter. Below is an actual picture of the Michelson Interferometer that we used to accumulate our data: The light originates from some source and is incident from the left. The interference pattern can be observed where the white piece of paper is at the bottom of the picture. Continue below to observe actual fringe patterns acquired using this apparatus.

________________________________________ Some Data From Previous Experiments: ________________________________________   Here are some pictures of fringes, both hyperbolic and circular in nature, as predicted by the theory discussed earlier. The top pictures are the interference patterns of a HeNe laser, the bottom are of sulfur. Clearly, they coincide with what theory predicts. Using the HeNe laser as a reference, one can calibrate the Michelson interferometer so that it can be used to determine the unknown wavelength(s) of the Sodium light. This is possible because of orders of interference. From general wave theory, constructive interference occurs in half multiples of the wavelength. Using this relationship,, we can solve for the wavelength of light because this ratio represents the variable L.  Thus, to find the wavelength, let a motor drive the lever arm while a device is used to count the fringes that pass by (the variable n in the equation). Here are the results that myself and Dr. Von Seth Carpenter obtained while attempting this exercise: Stepping through the above data, we first determined how far the mirror traveled for a specific number of HeNe fringes to pass by. Since we knew the wavelength of a HeNe laser very precisely to be 632.8 nm, we used this relationship defined above solving for L. Next, we calculated the ratio of how far the lever arm moves in mm to how far the actual interferometer mirror gets displaced. This value allows one determine the unknown wavelength mostly because one determined the length L in terms of how far the mirror moves by looking at how far the lever arm turns. For sodium, we observed 210 fringes pass as the lever arm moved .315 mm. Again using our relationship for orders of constructive interference, we determine the unknown wavelength of sodium to be on the order of 606.905 nm. In looking at the American Institute of Physics Handbook, the most probable wavelength of light we should see is 589.5 nm with a 62.8% probability. The other line that we should have seen, but didn't was 588.9 nm with 63% transition probability. Our 606.905 nm calculated data is within -2.96% error. Finally, a phenomena that occurs with sodium, but not the HeNe light (because it is close one wavelength), are beats. Beats occur when two waves of different frequencies are travelling in the same direction and interact with each other. This means that they alternate between constructive and destructive interference because they are periodically out of phase. Since the sodium light is comprised of the two different wavelengths, 589.95 and 588.5 nm, it finds itself susceptible to this temporal interference.

________________________________________ Other Uses for the Michelson Interferometer: ________________________________________ This link reveals a new method for measuring gravity using convection currents in fluids. They use the Wave theory of light as it pertains to light passing through these convection currents with different indices of refraction...pretty cool stuff. NASA sponsored it so you know its ripe. Check it out here. Here, the Michelson Interferometer is used to measure trace gases in our atmosphere by Passive Atmospheric Sounding. You can see it here.

Textbook(s) (Typical):

Materials Science and Engineering: An Introduction, 6th Edition, William D. Callister, Jr., John Wiley, 2003

Introduction to Materials Science for Engineers, 6/E, James F. Shackelford, Prentice Hall, 2005

The Science and Engineering of Materials 4th Edition ,Donald R. Askeland, Pradeep P. Phulé, Thomson-Brooks/Cole, 2003

Foundations Of Materials Science And Engineering, Third Edition, William F. Smith, McGraw-Hill, 2004

Fundamentals of Materials Science and Engineering: An Integrated Approach, 2nd Edition, William D. Callister, Jr., John Wiley, 2004

07.04.2010.

1.Absorption 2.Albedo Area Brittleness Boiling point capacitance color concentration Conduction Density Dielectric ductility diffusion distribution of atoms efficiency electric Charge Electric field. Potential

Mathematics

Space curves arc length tangent normal space binormal curvature curves surfaces tangent surfaces involute evolute intrinsic equations helices curves on surfaces surface of revolution helicoids matrices & direction coefficients families of curves isometric correspondance geodesics canonical geodesic equations normal property of geodesics existance theorems geodesic parallels geodesic curvature surface of constant curvature conformal mapping principle curvature line of curvature devolapables associated with space curves curves on a surface minimal surfaces ruled surfaces fundamental equations of surface parallel theory of surfaces general solution for homogeneous differential equation use of known result to find unknown the homogeneous equation with constant coefficients method of undetermined coefficients variation of parameters vibration in mechanical systems newton's law of gravitation and the motion of planets power series and their solutions ordianary points regular singular points gauss hypergeometric equations the point at infinity Legendre polynomials Properties of legendre polynomials Bassel's functions Gamma functions Group theory Normal sub groups Quotient groups homomorphisms automorphisms cayley's theorem Permutation groups Counting principles Sylow's theorem Rings Ideals Quotient rings Integral domains Eucleadian rings polynomial rings polynomials over rational fields and commutative rings vector spaces and modules dual spaces extension fields roots of polynomials elements of Galois theory Solvability by radicals Galois group over the rationals Algebra of linear transformations Characteristic roots Matrices and their forms Traingular form Canonical form Jordan form Nilpotent transformations Hermitian transformations

Unitary transformations Normal transformations Real quadratic forms Finite fields Wedderburn's theorem Finite division rings Darivatives and continuity algebra of derivatives Functions with non zero derivatives Rolle's theorem Mean value theorem Taylor's formula with remainder properties with monotonic functions functions of bounded variation The Reimann-Steltjes integral Sequences of functions Measure theory Lebesgue integral infinite product gamma functions tests of convergence Rearrangement of factors in product Tennery theotem Hyperbolic function Bernouli's numbers

Physics

Review of Newtonian mechanics, inertial frames of reference; Galilean Principle of Relativity; non-inertial frames. Generalised co-ordinates, the Principal of Least Action, the Lagrangian. Motion in one dimension and turning points - relation between the potential energy and the period of motion. The two-body central force problem, Kepler motion. Small oscillations, normal modes, forced and damped oscillations under friction- non-linear oscillators, perturbation theory and parametric resonance, motion in a rapidly oscillating field. Rigid body motion- Euler’s angles and equation - the asymmetric top. Collision theory - scattering, small angle scattering, Rutherford’s formula. Hamiltonian formulation, canonical transformations, Poisson brackets. Liouville’s theorem Hamiltonian-Jacobi theory, Action-Angle variables. Phase space, phase space trajectories, fixed points and their stabilities. Vector analysis, Green, Gauss and Stokes theorems. Linear vector spaces and linear operators. Matrices & eigenvalue problem. Theory of complex variables, Cauchy-Riemann conditions, Cauchy integral theorem, Taylor- Laurent expansion, classification of singularities, analytic continuation, theorem of residues and evaluation of definite integrals and series. Ordinary differential equations and series solution. Sturm-Liouville problem and orthogonal functions, special functions. Green’s functions for self-adjoint differential operators and eigenfunction expansion. (Laplace, Poisson, Diffusion, Wave equation etc to be discussed). Need for Quantum Mechanics. Operators and Linear Vector Spaces to describe observables and states of a system. Eigenstates and eigenvalues. Expansion into eigenstates and probabilistic interpretation. Canonical commutation relations. Uncertainty principle. Position and momentum representations. Wavefunctions. Schr¨odinger and Heisenberg equations of motion. Probability density and probability current densities. Ehrenfest Theorem. Stationary states; Non-stationary states: as examples Gaussian and Airy wave-packets for a free particle. Time-independent Schr¨odinger equation. One dimensional problems: bound states, reflection and transmission, linear harmonic oscillator, the coherent state, tunnelling through potential barriers and examples. Illustrations from mesoscopic physics, quantum wires etc Motion in three dimensions. Central potential problems (bound states in 3D). Symmetry in quantum mechanics. Angular momentum and spin; Addition of angular momenta. Electrostatics & methods of solving boundary value problems, Multipole expansion of electrostatic potentials. Dielectrics. Biot-Savart Law & Ampere’s Law. Vector potential. Faraday’s Law and time-varying fields. Maxwell’s equations, energy and momentum of the electromagnetic field, Poynting Vector, Conservation Laws. Introduction to Fortran programming and basic numerical methods will be imparted to the students through lectures and projects based on the numerical analysis of elementary physical problems illustrating such techniques. Review of thermodynamics. Need for statistical mechanics. Basic ideas of probability and statistics, random walks, Gaussian and Poisson Distributions, Central Limit Theorem. Distribution functions and phase space. Liouville equation, mixing and ergodicity. Ensembles: Micro canonical, Canonical, Grand canonical. Partition function - connection with thermodynamic potentials Quantum Ideal Gases - Fermi-Dirac/Bose-Einstein Statistics. Various applications of ideal fermions to specific heat and susceptibility of metals, etc. Various applications of ideal bosons to black body radiation and Planck distribution, etc. Imperfect gases. Basic ideas of phase transitions. Elements of Group Theory. Fourier and Laplace transforms, Saddle point method and asymptotic expansions. Integral Equations Calculus of Variations. Functional integration and functional differentiation. Scattering theory - Born approximation and partial wave analysis. Time independent perturbation theory. Variational method The WKB approximation. Time independent perturbation theory (Fermi’s Golden Rule). Adiabatic and Sudden Approximations Geometric Phases and the Bohm-Aharanov Effect. Rotation group, Tensor operators and the Wigner-Eckart theorem. Illustrations from atomic, molecular and nuclear physics. Pure and Mixed states. Density Matrix formalism Lorents Invariance of Maxwell’s equations; Review of Special Relativity; Maxwell’s equations in covariant form; four-vector potential and the electromagentic field tensor. Propagation of plane electromagnetic waves, reflection and refraction. Propagation through anisotropic and chiral media. Radiation from an accelerated charge, retarded and advanced potentials. Radiation multipoles Wave guides, Resonant Cavities. Error analysis: Errors in observation and treatment of experimental data, estimation of error, theory of errors and distribution laws, least squares method, curve fitting, statistical assessment of goodness of fit. 2. Basic measurement techniques and the underlying physical principles • Low temperature • Low voltage • High vacuum 3. Spectroscopic techniques: Theory and experiments 4. Theory and experiments in Nanophysics Path Integral Formulation of Quantum Mechanics. Relativistic quantum mechanics : Klein-Gordon and Dirac equations. Relativistic hydrogen atom. Canonical quantization of fields : the Schr¨odinger field and its applications to many-body problems. (Illustration through superfluidity, superconductivity, hard-sphere bose gas etc.) Quantization of real and complex scalar fields, and the Maxwell field (non-covariant quantisation in the radiation gauge). Spontaneous and Induced Emission of Photon from Atoms. Covariant perturbation theory. QED at tree level and calculation of processes such a Compton scattering, Moller scattering, etc. Binding and cohesion in solids. Bonds and bands. Crystal Structure, X-ray Diffraction, Reciprocal Lattice. Periodic potentials, Bloch’s Theorem, Kroning Penney Model, Free electrons and nearly free electrons; tight binding approximation. Elementary ideas of band structure of crystalline solids. Concept of holes and effective mass; density of states; Fermi surface; explanation of electronic behaviour of metals, semi-conductors and insulators. Lattice vibrations, harmonic approximation, dispersion relations and normal modes, quantization of lattice vibrations and phonons. thermal expansion and need for anharmonicity. Transport properties of solids. Boltzmann transport equation. Wiedemann-Franz law. Hall effect. Superconductivity: Phenomenology, penetration depth, flux quantization etc. Josephson effect. Semiconductors: intrinsic and extrinsic, carrier mobility etc. Thermal properties of solids. Magnetism in solids. Accelerators Passage of Radiation through matter Detectors The nuclear two-body problem The Liquid Drop Model. The Shell Model. The Collective Model. Beta decay of nuclei. Gamma decay of nuclei. Relativistic notations. SU(2) and the rotation group. Lorentz Group and SL(2,C). Homogeneous and Inhomogeneous Lorentz Group and their Algebras. Spinors. Relativistic Covariant Equations- Klein Gordon, Dirac and Maxwell equations. Quantization of free fields: Canonical and Path Integral Approach. Covariant quantisation of the Maxwell field. Interacting Fields and the Gauge Principle. Feynman-Dyson Perturbation Expansion and Feynman Diagrams. Quantum Electro-Dynamics. Tree Level Calculations of Compton Scattering Cross-section etc. Loops, Divergences, Regularization and Renormalization. Anomalous magnetic moment of the electron and the Lamb-Shift. Special theory of relativity. Tensor analysis. Covariant and contravariant tensors. Metric tensor. Affine connection and curvature tensor. Bianchi identities. General theory of relativity. Equivalence principle. Principle of general covariance. Geodesics and equation of motion of particles. Gravitational field equations. Schwarzschild solution. An introduction to the standard big-bang cosmological model. Cosmological principle. Robertson-Walker metric. Hubble’s law and red-shifting of light. Energy-momentum tensor for a perfect fluid. Equation of state and solution of Einstein’s equations for radiation, matter and vacuum energy. Cosmic microwave background radiation. Review of perturbation theory for time evolution operator (propagator) - interaction picture Time evolution in frequency (Fourier-Laplace transform domain) - resolvent expansion - Lippman-Schwinger equation - T matrix/multiple scattering theory. Finite temperature Green’s function - retarded case - application to superconductivity. Salpeter equation. Ward identitites and Feynman diagrams. Ring and ladder diagrams - Bethe-Bruckner-Goldstone theory. Coulomb interaction - Hartree-Fock theory - Random Phase Approximation (RPA). Electron-phonon (Frohlich) interaction - superconductivity. Superfluidity. Quantum Chemistry and the Nature of the Chemical Bond. Chemical Kinetics and Thermodynamics. Order of the Reaction. Rate laws. Mechanism of Chemical Reactions: (a) Collision Theory (b) Transition State Theory (c) Potential Energy Surface (d) Kramers Escape Rate. Enzyme Reactions: Solution kinetics, characterization of enzymes, control mechanisms. Electron Transfer: (a) Dynamical Electrochemistry (b) Electron Transfer (c) Quantum Models (d) Electron Charge Transfer in Proteins. Plasma State of Matter: Introduction Motion of a charged particle in electromagnetic field. Plasma as a fluid; elementary discussions on wave motion in plasma. Fluid nature of plasma, waves in a ”cold” plasma. Derivation of the general dispersion relation, different types of waves in plasma and their classification. Dispersion relations for different waves, Effects of finite temperature on wave propagation. Kinetic theory of Plasma. Elements of Magneto-hydrodynamics (MHD) Elements of Parametric excitation and nonlinear waves in Plasma. Experimental methods for measuring plasma parameters. Elementary ideas of confinement of high temperature plasma. Books Goldstein : Classical Mechanics Landau and Lifshitz : Mechanics Percival and Richards : Classical Dynamics Marion : Mechanics Hand and Finch, Analytical Mechanics. G. Arfken, Mathematical Methods for Physicists I.N. Sneddon, Special Functions of Mathematical Physics & Chemistry P.K. Chattopadhyay, Mathematical Physics E. Kreyszig, Advanced Engineering Mathematics Mathews and Walker, Mathematical Physics P. Dennery & A. Kryzwicki, Mathematics for Physicists C.M. Bender & S.A. Orszag, Advanced Mathematical Methods for Scientists & Engineers E. Butkov, Mathematical Physics R.W. Churchill & J.W. Brown, Complex Variables & Applications Merszbacher : Quantum Mechanics Sakurai : Modern Quantum Mechanics Cohen-Tannoudji, Diu and Lal¨oe, Quantum Mechanics I Schiff : Quantum Mechanics Landau and Lifshitz : Quantum Mechanics Messiah : Quantum Mechanics I and II Powell and Craseman : Quantum Mechanics K. Gottfried, Quantum Mechanics Bransden and Joachim, Introduction to Quantum Mechanics Townsend, Quantum Mechanics J.D. Jackson, Classical Electrodynamics J.R. Reitz, F.J. Milford & R.W. Christy, Foundations of Electromagnetic Theory. D.J. Griffiths, Introduction to Electrodynamics Price, Analog Electronics (Prentice-Hall) Hickman, Analog Electronics (Newnes) Bogart, Electronic Devices and Circuits (Universal Book Stall) Streetman, Solid State Electronic Devices (P/H/I) Horowitz and Hall, The Art of Electronics (Cambridge) Callan, Introduction to Thermodynamics & Thermostatistics F. Reif, Fundamentals of Statistical & Thermal Physics R.K. Pathria, Statistical Mechanics L.E. Reichl, A Modern Course in Statistical Physics Kerson Huang, Statistical Mechanics Landau & Lifshitz: Quantum Mechanics Messiah, Quantum Mechanics I & II Davidov, Quantum Mechanics Sakurai : Modern Quantum Mechanics Cohen-Tannoudji, Diu & Lal¨oe, Quantum Mechanics II Ryder, Quantum Field Theory Flugge, Practical Quantum Mechanics J.D. Jackson, Classical Electrodynamics J.R. Reitz, F.J. Milford & R.W. Christy, Foundations of Electromagnetic Theory. Dekker, Solid State Physics Kittel, Introduction to Solid State Physics Ashcroft and Mermin, Introduction to Solid State Physics. Ziman, Principles of the Theory of Solids. Subatomic Physics, H. Frauenfelder and E.M. Henley, Prentice Hall 1974. W.E. Burcham and M. Jobes, Nuclear and Particle Physics, Addison Wesley 1998 Pooh, Rith, Scholz and Zetsche, Particles and Nuclei, Springer 1995. D.H. Perkins, Elementary Particle Physics A. Preston & A. Bhaduri, Nuclear Physics S. Weinberg, Gravitation and Cosmology Misner, Thorne and Wheeler, Gravitation R. Wald, General Relativity. Kolb and Turner, Early Universe. A. L. Fetter and J. D. Walecka, Quantum Theory of Many Particle Systems G. D. Mahan, Many Particle Physics Mattuck, A Guide to Feynman Diagrams in the Many Body Problem Negele, P. Nozieres and D. Pines, The Theory of Quantum Liquids, Vols. I & II Principles of Plasma Physics, N. A. Krall and A. W. Trivelpiece, McGraw-Hill (1973) Introduction to Plasma Theory, D. W. Nicholson, John Wiley (1983) Introduction to Plasma Physics (2nd Ed), F. F. Chen, Plenum Press (1989) Plasma Physics - Basic theory with fusion application, (2nd Ed.) K. Nishikawa and M. Wakatani, Springer-Verlag (1994) Fundamentals of Plasma Physics (2nd Ed.), J. A. Bittencourt, (Published by Bittencourt (1995)) The Physics of Fluids and Plasmas, An Introduction for Astro Physicists, Arnab Raichaudhuri, Cambridge Univ. Press, First South Asian Ed. (1999) Chaikin & Lubensky, Principles of Condensed Matter Physics Hansen & Mcdonald, Theory of Simple Liquids De Gennes, Liquid Crystals Landau & Lifshitz, Theory of Elasticity Doi & Edwards, Polymers De Gennes, Scaling Concepts in Polymer Physics Solids Far From Equilibrium, ed. C. Godriche Baraban & Stanley, Fractal Properties of Surface Growth Debashish Chowdhury, Physics Reports. P. Bak, How Nature Works. A. Mehta, J. Preskill, http://www.theory.caltech.edu/people/preskill/ph229 A. Peres, Quantum Theory: Concepts and Methods. Electronic Structure of Solids and Alloys, eds. O.K. Andersen, V. Kumar, A. Mookerjee. (World Scientific) - Electronic Structure of Solids, O.K. Andersen, O. Jepsen (Proceedings of the Varenna School, 1983) - SERC School Lecture Notes, 2000, Calcutta : S.K. Ghosh, M. Harbola Phase Transformations, Ducastelle and Gautier Theory of Phase Transformations, Khatchaturyan, Rev. Mat.Science Spin Glasses, D. Chowdhury and A. Mookerjee, Physics Reports Spin Glasses, D. Chowdhury (World Scientific)

by

T.CHENGAPPA Department of Physics Indian Institute of Technology Hyderabad Andhra Pradesh

Physical Properties	Chemical properties	Thermal properties	Mechanical properties	Optical properties	Magnetic properties absorption Reactivity against other chemical substances	Thermal conductivity Young's modulus Permeability

albedo Heat of combustion	Thermal diffusivity Specific modulus Absorptivity Hysteresis

area Enthalpy of formation	Thermal expansion Tensile strength Reflectivity Curie Point

brittleness Toxicity	Seebeck coefficient Compressive strength Refractive index boiling point Chemical stability in a given environment	Emissivity Shear strength Color capacitance Flammability	Coefficient of thermal expansion Yield strength Photosensitivity color Preferred oxidation state(s)	Specific heat Ductility Transmittance concentration Coordination number	Heat of vaporization Poisson's ratio conductance Capability to undergo a certain set of transformations, for example molecular dissociation, chemical combination, redox reactions under certain physical conditions in the presence of another chemical substance	Heat of fusion Specific weight density Preferred types of bonds to form, for example metallic, ionic, covalent	Pyrophoricity dielectric pH Flammability ductility Hygroscopy Vapor Pressure distribution Surface energy Phase diagram efficacy Surface tension Binary phase diagram electric charge Specific internal surface area Autoignition temperature electric field Reactivity Inversion temperature electric potential Corrosion resistance Critical temperature emission Glass transition temperature flow rate Eutectic point fluidity Melting point frequency Vicat softening point impedance Boiling point inductance Triple point intensity Flash point irradiance Curie point length location luminance luster malleability magnetic field magnetic flux mass melting point moment momentum permeability permittivity pressure radiance solubility specific heat resistance reflectivity spin strength temperature tension thermal transfer velocity viscosity volume ______________________________________ The Michelson Interferometer ________________________________________

History: ________________________________________  Back in the early days, the only waves that people could observe were those travelling in some sort of medium. For example, the waves in a river or the ocean were seen travelling in water. Therefore, there natural conclusion to be made by many people (Most importantly Huygen) that light, if it were to be a wave, and it had been proven to exhibit characteristics of them, would have to be travelling in some medium. As history would dictate, this mysterious medium that nobody could perceive with their senses or instrument, would be deemed the "luminiferous ether". Light, as well as all of the solar systems in the universe were said to be ensconced in this ether which would have to maintain a wave speed of 3e8 m/s (according to Maxwell's predictions at the time). The team of the two professors,  Michelson and Morley, would attempt to detect the presence of the elusive ether in 1880. To do so, they devised the interferometer which would allow them to observe the effect of the motion of the medium upon the propagation of light. Hence, interferometry was born around the famous "null outcome" experiment performed by Michelson and Morley in the late nineteenth century. ________________________________________ Theory of the Michelson Interferometer: ________________________________________   The picture below represents an interferometer in its simplest form: A source S emits monochromatic light that hits the surface M at point C. M is partially reflective, so one beam is transmitted through to point B while one is reflected in the direction of A.  Both beams recombine at point C to produce an interference pattern (assuming proper alignment) visible to the observer at point E.  To the observer at point E, the effects observed would be the same as those produced by placing surfaces A and B' (the image of B on the surface M) on top of each other. Let's look at this interaction in more detail. Imagine that we two surfaces M1 and M2 as diagramed below: The light of interest originates at point S until it comes into contact with the two surfaces (we assume the angles of incidence are the same) and is reflected to point P. Here theta is the angle of incidence for the light, t represents the separation of the two surfaces, and phi is the angle between them which can be assumed small enough to ignore. The difference in paths of the two beams, delta, originating at S can then be described by. If we make the intersection of the planes M1 and M2 be vertical, the distance between the mirrors to P is d, and the angle between the normal to M1 i, then the above expression can be written as  (assuming i is small). Now one can write an expression for the phase difference for the light, alpha,. This equation, however, presents quite a wide range of values for the phase which might make it impossible, or at least very hard to observe interference phenomena because we want the phase difference to be small (see my explanation why in the discourse on light basics). Therefore, delta must be for a particular change in the angle of incidence, theta. This modification can be done by taking the derivative of delta with respect to theta and setting it equal to zero. In doing so, we find that the different parts of the interference pattern can't be seen unless the distance between the two planes M1 and M2, t0 ,is zero when d=0 (case where interference effects are localized at M1 and M2), or if the angle between the two plane surfaces is zero and P=infinity. Intuitively, this makes sense because the smaller the distance between the two planes, the smaller the distance for the phases of the two rays to get less uniform. From this situation, it also becomes possible to determine the shape of the interference effects. As it turns out, the effects are either linear or circular patterns. Lets redraw the coordinate above to see mathematically how to obtain these fringe patterns (i.e. the situation pictured below). One now looks at the two planes from the front instead of the side. The observer resides at point O, R is the base of the perpendicular from O onto the plane M1, and the ray OR=z. The path difference, as we have proved above, from M1 to M2 is. The ray OP is the hypotenuse of the triangle OPR so it is equal to. The cosine of the angle theta, which will be important in a moment, can then be expressed as. The surface thickness at point R will be designated "e", so at the point P(x,y)  the thickness is defined to be , where alpha is the angle that separates the two planes (It was phi in the diagram above it). For stationary waves, the normal modes occur at integer multiples of the lights' wavelength given by the following formula. If we had a wave on a string, L would the length of the string itself. In our case, however, it is the distance from the plane M2 to the plane M1. Thus, this distance. Now we can write an expression that governs the behavior of the fringes that we see at point O. This relationship is. Consider the two important cases that determine the shape of the interference patterns observed at point O. The first case occurs when both M1 and M2 intersect at the perpendicular, point R.  Here the thickness of the surfaces, e, is zero. Thus, the  fringe determining equation is rearranged to. The relationship was able to be reduced by making the assumption that z >>x+y and alpha is small. The resulting expression is that of a line with fringes separated by distance. Interestingly enough, if the observer is too close to the surface planes M1 and M2, this assumption can't be made. The result is a hyperbolic function causing the fringes to appear slightly bent. The second case to be considered appears when the two surface planes are parallel to each other (i.e. the angle alpha between them is zero). Thus,our fringe governing equation gets rearranged yet another time to yield: Clearly this represents the equation of a circle, hence our fringes appear circular to the observer. One more important point to remember is the property of coherence length when it comes to a device that studies interference effects. If the differences in path length to both the mirrors and back from the beamsplitter is greater than the coherence length, then no interference effects will be seen. Thus, when adjusting the moveable mirror on the Michelson interferometer, one must be precise when trying to find interference patterns of light comprised of a large difference in wavelengths, such as white light. Now that you understand how we get these fringes, lets see if we can reproduce them with a Michelson Interferometer! ________________________________________ Studying the Wave Nature of Light with a Michelson Interferometer: ________________________________________   The Michelson Interferometer represents a device that takes advantage of the Wave Nature of Light. If light were not to be considered a wave, none of the observed interference patterns could occur in experiments as they do. In this section, how light can interact and interfere with itself to produce these fringes and patterns characteristic those of waves is described. Below (thanks to my partner on the project that we performed this semester, Seth Carpenter) we see an interferometer a little more complex than that used in the theory discussion. The main difference between the one used to derive theory and the one picture above, is the addition of the "compensatory lens". This lens is added so that both paths, from the back of beam splitter to Mirror 1 and Mirror 2, are identical. This addition becomes necessary since the back of the beam splitter is where the light gets reflected (usually by a partially reflective silver coating). Thus, the light travelling to Mirror 1 travels through the thickness of the beamsplitter 3 times; once as it enters initially, next as it is reflected off the back of it, and finally as it returns to the beamsplitter after reflecting off of Mirror 1. If the compensatory lens were not in place, the light travelling to Mirror 2 would only travel through the beamsplitter once since it is transmitted through it and then reflected off the back of it. Therefore, the compensatory lens MUST be of exactly the same thickness as the beam splitter. Below is an actual picture of the Michelson Interferometer that we used to accumulate our data: The light originates from some source and is incident from the left. The interference pattern can be observed where the white piece of paper is at the bottom of the picture. Continue below to observe actual fringe patterns acquired using this apparatus.

________________________________________ Some Data From Previous Experiments: ________________________________________   Here are some pictures of fringes, both hyperbolic and circular in nature, as predicted by the theory discussed earlier. The top pictures are the interference patterns of a HeNe laser, the bottom are of sulfur. Clearly, they coincide with what theory predicts. Using the HeNe laser as a reference, one can calibrate the Michelson interferometer so that it can be used to determine the unknown wavelength(s) of the Sodium light. This is possible because of orders of interference. From general wave theory, constructive interference occurs in half multiples of the wavelength. Using this relationship,, we can solve for the wavelength of light because this ratio represents the variable L.  Thus, to find the wavelength, let a motor drive the lever arm while a device is used to count the fringes that pass by (the variable n in the equation). Here are the results that myself and Dr. Von Seth Carpenter obtained while attempting this exercise: Stepping through the above data, we first determined how far the mirror traveled for a specific number of HeNe fringes to pass by. Since we knew the wavelength of a HeNe laser very precisely to be 632.8 nm, we used this relationship defined above solving for L. Next, we calculated the ratio of how far the lever arm moves in mm to how far the actual interferometer mirror gets displaced. This value allows one determine the unknown wavelength mostly because one determined the length L in terms of how far the mirror moves by looking at how far the lever arm turns. For sodium, we observed 210 fringes pass as the lever arm moved .315 mm. Again using our relationship for orders of constructive interference, we determine the unknown wavelength of sodium to be on the order of 606.905 nm. In looking at the American Institute of Physics Handbook, the most probable wavelength of light we should see is 589.5 nm with a 62.8% probability. The other line that we should have seen, but didn't was 588.9 nm with 63% transition probability. Our 606.905 nm calculated data is within -2.96% error. Finally, a phenomena that occurs with sodium, but not the HeNe light (because it is close one wavelength), are beats. Beats occur when two waves of different frequencies are travelling in the same direction and interact with each other. This means that they alternate between constructive and destructive interference because they are periodically out of phase. Since the sodium light is comprised of the two different wavelengths, 589.95 and 588.5 nm, it finds itself susceptible to this temporal interference.

_______________________________________ Other Uses for the Michelson Interferometer: ________________________________________ This link reveals a new method for measuring gravity using convection currents in fluids. They use the Wave theory of light as it pertains to light passing through these convection currents with different indices of refraction...pretty cool stuff. NASA sponsored it so you know its ripe. Check it out here. Here, the Michelson Interferometer is used to measure trace gases in our atmosphere by Passive Atmospheric Sounding. You can see it here.