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PROGRAM STRUCTURE MSc: (Physics) by - Research SEMESTER- I Course Code PY2314 PY 2312 PY 2214 PY 2353 PY 2232 PY 2331 Exam Duration (Hrs) Course Name L T P C Theory Atomic, Molecular & Laser Physics Nuclear Physics Solid State Physics Program Elective-I: NanoScience and NanoTechnology- I Spectroscopy Lab Solid State Physics Lab Total Credits 2 1 0 3 3 3 3 3 1 1 1 0 0 0 4 4 4 3 3 3 - 10 10 10 - 0 0 11 0 0 4 6 6 12 3 3 21 - 4 4 - 60 60 SEMESTER- II Course Code PY 2113 PY 2212 PY 2411 PY 2454 PY2180 PY 2132 PY 2431 Practical Relative Weightage (%) CWS 10 Exam Duration (Hrs) PRS MTE T 40 40 40 40 ETE PRE 50 50 50 50 - - 40 40 Relative Weightage (%) Course Name L T P C Theory Practical CWS PRS T - Electronics Quantum Mechanics Nuclear and Radiation physics PE-II : Nanoscience and Nanotechnology-II Seminar Electronics Lab Nuclear Physics Lab Total Credits 3 3 3 1 1 1 0 0 0 4 4 4 3 3 3 - 10 10 10 3 1 0 4 3 - 10 - 0 0 0 12 0 0 0 4 4 6 6 16 2 3 3 24 - 1 4 4 - 60 60 60 MTE ETE PRE 40 40 40 50 50 50 - 40 50 - - 40 40 40 - SEMESTER- III Course Code PY 2381 PY 2111 PY 2380 Exam Duration (Hrs) Course Name L T P C Theory Practical CWS Project I Mathematical Physics* Seminar 3 0 1 0 0 2 20 4 1 3 2 1 10 - Total Credits *Self Study course 25 SEMESTER- IV Course Code PY 2481 PY 2211 PY 2480 Relative Weightage (%) Course Name Project II Classical Electrodynamics* Seminar Total Credits *Self Study course Total Credit: 100 ETE PRE 50 - 40 40 - Exam Duration (Hrs) Relative Weightage (%) L T P C Theory Practical CWS 3 1 0 24 4 3 2 - 10 0 0 4 2 1 - 30 PRS MTE T 60 40 60 - - PRS MTE T 60 40 60 - ETE PRE 50 40 - - 40 L = Number of Lectures hrs/week T= Number of Tutorials hrs/week P = Number of practical hours/week C= Number of Credits. CWS: Class Work Sessionals PRS: Practical Sessionals MTE: Mid-Term Exam ETE: End Term Exam PRE: End Term Practical Exam * Presentations Only First Semester PY2314 Atomic, Molecular and Laser Physics [3 1 0 4] Spectra of single & Multi electron atoms: H-atom, relativity and spin Correction, Central Field Approximation (CFA), L-S and J-J coupling approximation, spectral terms :(i) atoms with two or more non-equivalent optical electrons, Lande`s interval Rule, Normal and inverted multiplets, order of terms and fine structure levels, selection rules for multi electron atoms in LS coupling and J-J coupling. Spectra of alkali elements: Fine structure and intensity ratio for doublets, spectra of alkaline earth elements, interaction energies in L-S and J-J coupling, comparison of terms, spectra of elements with “P” configuration, spectra of elements with unfilled d & f – shells. Molecular spectra: Rotational & vibrational spectra for diatomic molecules, Electronic spectra of diatomic molecules, vibrational coarse structure, Frank–Condon principle, Dissociation energy & products, Rotational fine structure of electronic vibration transitions, Electronic angular momentum in diatomic molecules, Raman Spectroscopy. Atoms in external fields (Electric & Magnetic) : The normal Zeeman effect, Weak fields, Russel–Saunder`s terms and general case, Intensity of lines in Weak fields and Quadrupole lines, Paschen back effect, Stark effect, Linear stark effect, illustration for H-atom & series limit, theory for nonhydrogenic atoms- He & Alkali metals. Spectrographs: Working principle of spectroscopic instruments for UV- Vis- IR region and applications. Laser Physics: Basic elements of Laser, Threshold condition, 4-level Laser system, CW operation of Laser, critical pumping rate, population inversion & photon number in the cavity around threshold, output coupling of Laser power. Optical resonators, cavity modes, mode selection, pulsed operation of Laser, Q- switching and mode locking; Experimental technique of Q- switching & mode locking. Laser systems: Ruby, Co2, Dye & Semiconductor diode Laser. Holography: Basics, recording and reconstruction of reflection hologram, simple applications. Text/Reference Books: 1. Sobel`man : introduction to the theory of atomic spectra, Wiely, (2008). 2. E.V. condon & G.H. Shortley: Theory of Atomic Spectra, Cambridge University Press (1935) 3. G. Hertzberg : Atomic spectra & atomic structure power publication, Dover Publications, Inc., New York, 1944) 4. G. Aruldas, Molecular structure & spectroscopy PHI, New Delhi(2001) 5. Colin N. Banwell & Elaine M. Mccash: Fundamentals of Molecular spectroscopy, TMH publishing co. Ltd. IV edn. (2002) 6. Barrow G. M. , Introduction to Molecular Spectroscopy, Tata McGraw Hill (1962). 7. Molecular spectra & Molecular structure G: Hertzberg, di Lauro, Carlo, Elsevier (2013) 8. Laser Theory & its application: Ghatak & Thyagarajan (Mcmillan), Plenum Publishing Corporation, New York , (1981). 9. Laud B.B. ,Laser & Nonlinear optics, Wiley Eastern, II edition,(1991) . 10. White, H. E., Atomic Spectra, TMH (1934). PY 2312 NUCLEAR PHYSICS [3 1 0 4] Properties of Nuclei & Nuclear Forces Nuclear Mass, Nuclear Binding Energy Nuclear radius, Spin and magnetic moments of Nuclei, Parity, Angular Moment, Electric Um Quardrupole moments, Concept of meson theory of Nuclear forces, Exchange Force andTensor Force. Charge independence and Charge symmetry of nuclear forces. Isospin formalism. Nuclear Interaction Bound State of two nucleons, Theory of Ground State of two nucleons. Nucleon- nucleon scatterings (n-p & p-p) at Low energies (<10MeV). Scattering Length. Effective range theory in n-p and p-p scattering, Spin dependence of nuclear forces. Scattering of Neutrons by ortho and para hydrogen molecule Nuclear Reactions Classification of nuclear reactions – Direct and Compound nuclear reaction mechanisms. Scattering and reactor cross sections by partial wave analysis, Bohr’s theory of compound nucleus. Resonance reaction and Briet-Winger one level formula. Bohr-Wheeler theory of fission& Nuclear Reactors. Nuclear Models Shell model - Experimental evidence for shell effects and magic numbers, Shell model spin orbit coupling. Schmidts lines and prediction of angular momentum and parity of nuclear ground states. Collective model of Bohr and Mottelson – rotational States and Vibrational levels, Nilsson Model. Elementary Particles and their classifications. Elementary Particles and their classifications, conservation laws, parity conservation and violation, conservation of isotopic spin, Gell Mann Nishigima scheme,Charge conjugation and time reversal, CP violation and CPT theorem. Strong, Weak and electromagnetic interactions : coupling constants, decay life times and cross sections. Text and Reference Books: 1. Roy R.R. and Nigam B.P., Nuclear Physics, New age International, (1996) 2. Halliday D., Nuclear Physics. Wiley, 5th ed, (2001) 3. Enge H.A., Introduction to Nuclear Physics, Addison Wesley, 1 st ed, (1996) 4. Fermi E., Nuclear Physics, University of Chicago press, (1974) 5. Kaplan I Nuclear Physics, Addison Wesley, 2 nd ed, (1962) 6. Cohen B.L., Concepts of Nuclear Physics, Tata Mc- Graw Hill, 1st ed., 1971 7. Brown G.E. and Jackson A.D., Nuclein-Nucleon interactions, North Holland Publication, (1976) 8. Benedetti Side, Nuclear Interactio, John Wiley & Sons, 2 nd ed, (1966). 9. Bohr and B.R. Mottelson, Nuclear Structure, Vol.1 and Vol.2 , WA Benjamin, (1975). 10. Evans R.D. Atomic Nucleus, Krieger Pub. Company, (1982). PY 2214 SOLID STATE PHYSICS [3 1 0 4] Crystal Physics and X-ray Crystallography: Crystal solids, unit cells and direct lattice, two- and three-dimensional Bravais lattices, crystal systems, crystal planes and Miller indices, close packed structures, symmetry elements in crystals.Reciprocal Lattice and Experimental X-ray diffraction Techniques: Reciprocal lattices Bragg`s Law of diffraction, X-ray single crystal diffractometer Ewald Sphere, powder X-ray diffraction technique, structure factor. Semiconductors: law of mass action, calculation of impurity conductivity, ellipsoidal energy surfaces in Si and Ge, Hall effect, recombination mechanism. Lattice Vibrations and Thermal Properties: Interrelations between elastic constants ,vibrations of linear mono and diatomic lattices, Determination of phonon dispersion by inelastic scattering of neutrons. Electronic Properties of Solids: Electrons in periodic lattice: Bloch theorem, NFE model the Kronnig Penny model, classification of solids on the basis of band theory, effective mass, Fermi surface and Fermi gas, Hall Effect, Superconductivity Magnetic Properties of Solids: Classification and general properties of magnetic materials, Weiss theory of ferromagnetism, temperature dependence of spontaneous magnetization, Heisenberg’s model and molecular field theory, curie-Weiss law for susceptibility. Superconductivity: Experimental results: Meissner effect, nuclear spin relaxation, Giver and AC and DC, Josephson tunnelings. Text and Reference Books: 1. Azaroff, Introduction to Solids, Mc Graw hill, (1984) 2. Verma and Srivastava, Crystallography for Solid State Physics, New age publication, 1991 3. Kittle, Solid State Physics, Wiley, 8th ed., (2004) 4. Wahab M.A., Solid State Physics, Alpha Science international Ltd, 1 st ed, (2011) 7. Chaikin and Lubensky, Principals of Condensed Mater Physics, Cambridge University Press, (2000) PY 2353 NANO SCIENCE AND NANOTECHNOLOGY-I [3 1 0 4] Emergence of Nanotechnology Nanotechnology Timeline and Milestones, Overview of different nanomaterials available, Schrodinger equation, Electron confinement, Tunnelling of a particle through potential barrier, Density of states (0D, 1D, 2D, 3D) Synthesis of Nanomaterials Introduction, mechanical method, method based on evaporation, sputter deposition, CVD electric arc deposition, Ion beam techniques, Novel physical chemistry related to nanoparticles such as colloids and clusters, Exploitation of self-assembly and selforganization to design functional structures in 1D, 2D or 3D structures. Examples to emphasize on self-assembled monolayers, Role of polymers in lithography resists, Nanomaterials (Nanoparticles, nanoclusters, quantum dots synthesis): Preparation and Characterization: “Top-Down” and “Bottom-Up” approaches of nanomaterial (nanoparticles, nanoclusters and quantum dots) synthesis: Top-down techniques: photolithography, optical lithography Bottom-up techniques: self-assembly, self-assembled monolayers, Combination of Top-Down and Bottom-up techniques: current state-of-the-art. L-B methods, Sol-Gel method. Introduction of Nanoelectronics Metals and insulators, Semiconductors: classification, electrons and holes, transport properties, size and dimensionality effects, Quantum size effects in semiconductor quantum dots and nanowires, Introduction to single electron transistors (SETs): quantum dots, single electron effects, Coulomb blockade. Text and References Books: 1. Introduction to Nanotechnolology – Charles P. Poole Jr. et.al John Wiley & Sons, (Asia) Pte. Ltd, (2010) 2. Nanotechnology: Principles and Practices – Sulabha K. Kulkarni, Delhi, (2007) 3. Nanostructures and Nanomaterials: Synthesis, Properties and Application, Guozhong Cao, Imperial College Press, UK., (2004) 4. Nanostructured Materials and nanotechnology, Editor Hari Singh Nalwa, (Concise Edition) Academic Press. (2001) PY 2232 Spectroscopy lab [0 0 8 4] [Minimum 10 experiments to be performed] 1. Hydrogen spectra - determination of Rydberg constant 2. Absorption spectrum of iodine- determination of dissociation energy of I2 3. Study of the arc spectra of iron, copper, Zinc and brass 4. Identification of elements by spectroscopic method. 5. Study of normal Zeeman effect 6. Measurements of wavelength of He-Ne laser light using ruler. 7. Hyperfine structure of spectral lines using FP etalon/LG plate. 8. GM counters characteristics. 9. AIO bands-photographing and analysis 10. Analysis of the given vibration-rotation spectrum 11. Interpretation of a Raman and IR spectra of simple of triatomic molecules 12. Dissociation energy of diatomic molecules- comparison of different Spectroscopic methods 13. Analyses and, Identification of substances using XRD patterns using ASTM cards. 14. Identification of elements from stellar spectra 15. Gaussian power distribution law using lasers. 16. Determination of Curie temperature. 17. Compton spectrometer using microwave and “ Tennis ball “ model. PY - 2331 Solid State Physics Lab [0 0 6 3] 1. Determinations of Lande’s ‘g’ factor for l RRH crystal using electron spin resonance spectrometer (Electron Spin Resonance-ESR) 2. Determination of Fermi energy of metals 3. PN Junction Capacitance 4. Determination of transition temperature in ferrites 5. Magnetic susceptibility experiment using Quinke’s tube 6. Calibration of silicon resistance thermometer and measurement of temperature from 77K to room temperature 7. Measurement of magneto resistance 8. Determination of transition temperature in ferroelectrics 9. Dispersion relation and cutoff frequency in the case of a mono-atomic lattice using lattice dynamics kit 10. Dispersion relation, acoustical mode and optical mode of a diatomic lattice using lattice dynamics kit. Semester- II PY 2113 ELECTRONICS [3 1 0 4] Network analysis Review of network analysis and theorems. Thevenin’s theorem, Norton’s Theorem, Superposition Theorem, Maximum power transfer Theorem. Semiconductor devices and circuits Characteristics of a pn junction. Clipping and clamping circuits. Response of RCdifferentiator and integrator circuits for sine, square and ramp wave signals. BJT, JFET and MOSFET devices. Voltage divider bias. Small signal analysis of BJT and FET amplifiers in CE/CS configuration. Comparison of CE/CS configuration with CB/CG and CC/CD configurations. Frequency response of BJT amplifier. UJT characteristics and its use in a relaxation oscillator. SCR characteristics and its use in ac power control. Operational amplifiers and circuits BJT differential amplifier. Operational amplifier - voltage/current feedback concepts (series & parallel). Inverting and noninverting configurations. Basic applications of opamps - comparator and Schmitt trigger. IC555 timer - monostable and a stable multivibrators. Crystal oscillator using opamp. Voltage regulator using series transistor and opamp with current limiting facility. Three terminal IC regulators. Switch mode power supply (block diagram). Digital electronics Review of number systems, logic gates, latches and flipflops.. Simplification of logic functions by Karnaugh maps. Tristate devices. Decoders and encoders. Multiplexers and demultiplexers with applications. Synchronous counter design. Digital to analog conversion with R/2R network. Analog to digital conversion using flash technique. Reference Books: 1. Hayt W H, Kemmerly J E and Durbin S M, Engineering Circuit Analysis, VI Edn, McGraw-Hill (2002). 2. Boylestad R L, Introductory Circuit Analysis, VIII Edn, Prentice Hall (1997). 3. Boylestad R L & Nashelsky L, Electronic Devices & Circuit Theory, VIII Edn. Prentice Hall (2002). 4. Floyd T L, Electronic Devices, V Edn, Pearson Education Asia (2001). 5. Gayakwad R A, Opamps and Linear Integrated Circuits, III Edn. PHI (1993). 6. Floyd T L, Digital Fundamentals, VII Edn, Pearson Education Asia (2002). PY 2212 QUANTUM MECHANICS [3 1 0 4] General formulation of quantum mechanics Schrodinger wave equation - review of concepts of wave particle duality, matter waves, wave packet and uncertainty principle. Schrodinger’s equation for free particle in one and three dimensions - equation subject to forces. Probability interpretation of the wave function, probability current density - normalisation of the wave function, box normalisation, expectation values and Ehrenfest’s theorem. Representation of states, dynamical variables - Adjoint of an operator. problem - degeneracy. Eigenvalues and eigenfunctions. Eigen value The Dirac-delta function. Completeness and normalisation of eigen functions. Closure. Physical interpretation of eigen values, eigen functions and expansion coefficients. Momentum eigen functions. Stationary states and eigen value problems The time independent Schrodinger equation - particle in square well - bound states normalised states. Potential step and rectangular potential barrier - reflection and transmission coefficients - tunnelling of particles. Alpha decay.Simple harmonic oscillator Schrodinger equation and energy eigen values - Energy eigen functions. Properties of stationary states. Concept of parity. Rigid rotator. Particle in a central potential - radial equation.Three-dimensional square well. equation - energy levels. Stationary The hydrogen atom - solution of the radial state wave functions - bound states. Matrix formulation of Quantum Mechanics: Hermitian and unitary Matrices, Transformation and diagonalization of Matrics, Function of Matricies and matrices of infinite rank. Vector representation of states, transformation of Hamiltonian with unitary matrix, representation of an operator, Hilbert space.. Dirac bra and ket notation, projection operators, Schrodinger, Heisenberg and interaction pictures. Relationship between. Poisson brackets and commutation relations. Matrix theory of Harmonic oscillator Symmetry in Quantum Mechanics Unitary operators for space and time translations. Symmetry and degeneracy, Rotation and angular momentum; Commutation relations, eigenvalue spectrum, angular momentum matrices of J +, J-, Jz, J2. Concept of spin, Pauli spin matrices. Addition of angular momenta, Clebsch- Gordon coefficients and their properties, recursion n relations. Matrix elements for rotated state, irreducible tensor operator, Wigner-Eckart theorem. Rotation matrices and group aspects. Space inversion and time reversal: parity operator and anti-linear operator. Dynamical symmetry of harmonic oscillator. Applications: non-relativistic Hamiltonian for an electron with spin included. C.G. coefficients of addition for j =1/2, 1/2; 1/2, 1; 1, 1. Reference Books: 1. Powell and Crassman, Quantum Mechanics, Addison Wesley (1961). 2. Mathews P M and Venkatesan K, A Text Book of Quantum Mechanics, Tata McGraw Hill (1977). 3. Ghatak A K and Lokanathan S, Quantum Mechanics, III Edn., McMillan India (1985). 4. Sakurai J J, Modern Quantum Mechanics, Revised Edn., Addison Wesley (1994). PY 2454 -Program NANOSCIENCE AND NANOTECHNOLOGY- II [3 1 0 4] Characterization Techniques for Nanomaterials Characterization Techniques Related to Nanoscience and Nanotechnology: Compositional surface analysis: XPS, SIMS Microscopies: optical microscopy, fluorescence, TEM, SEM, Probe techniques: Scanning tunneling microscopy (STM), Atomic force microscopy (AFM), Neutron Scattering and XRD, Spectroscopic Techniques: UV-visible, FT-IR, Raman, NMR, ESR, Surface modification using ion beam, ion beam analysis technique: Secondary ion mass and RBS. Carbon Nanotubes and Fullerenes Synthesis and purification of carbon nanotubes, Single-walled carbon nanotubes and multiwalled carbon nanotubes, Structure-property relationships, Physical properties, Applications, Bucky Balls, Importance and Properties of fullerenes, Application of Fullerenes. Applications of Nanomaterials Garment industry, Rubber industry, Activated carbon industry, Electronics industry, Nanotechnology in Energy Conversion and Storage, Nanoelectronic Devices, Nanobiotechnology and Nanotechnology in Healthcare, Agricultural. References: 1. Introduction to Nanotechnolology – Charles P. Poole Jr. et.al John Wiley & Sons (Asia) Pte. Ltd. 2. Nanotechnology: Principles and Practices – Sulabha K. Kulkarni, Delhi. 3. Nanostructures and Nanomaterials: Synthesis, Properties and Application Guozhong Cao, Imperial College Press, UK. 4. Nanostructured Materials and nanotechnology, Editor Hari Singh Nalwa (Concise Edition) Academic Press. 5. Inorganic nanowires CRC Press M.Meyyappan and Mahendra K Surtkan PY 2411 Nuclear and Radiation Physics [3 1 0 4] Passage of Radiation through Matter Interaction of charged particles: Energy loss of charged particles through matter. Bethe block ionization formula. RangeEnergy relation. Multiple coulomb scattering -p ß measurements, Bremsstrahlung and Cerenkov radiations Interaction - stopping power - energy loss characteristics, particle range - energy loss in thin absorbers. Scaling laws. Interaction of fast electrons - specific energy loss. Electron range and transmission curves. Interaction of gamma rays: Interaction mechanisms - photoelectric absorption, Compton scattering and pairproduction. Gamma ray attenuation - attenuation coefficients, absorber mass thickness, cross sections. Interaction of neutrons - general properties - slows down interaction, fast neutron interaction, neutron cross sections. Radiation exposure and dose – dose equivalent. Nuclear detectors: Gas filled counters, Nuclear Emulsions, Gaseous Ionization Detector:- Ionization and Transport Phenomena in Gases, Transport of electrons and Ions in Gases. Avalanche Multiplication, GM Counters, Proportional counters, Multiwire proportional counters. Scintillation detectors - different types of scintillators - photomultiplier tubes, measurement with scintillation detectors - NaI(Tl), plastic scintillator - Scintillation spectrometer. Spectrum analysis. Semiconductor detectors : Semiconductor properties - physics of semiconductor detectors - diffused junction, surface barrier and ion-implanted detectors. Si(Li), Ge(Li) and HPGe detectors - semiconductor detector spectrometer. Pulse height analysis of spectrum, SSNTD, Superheated drop detectors. Neutron detectors - Neutron detection from nuclear TLD, reactions. BF3 counters, 3He counters, fission detectors, activation method for neutron flux measurement. Recoil counters - neutron time of flight technique Accelerating Machines and General Characteristics of Detector: Linear accelerators, Principle of orbital accelerators, Cyclotron, synchro-cyclotron, modification with reference to magnetic field and frequency, Beam Collider. Detector properties: - Sensitivity, Detector response, Energy resolution Response function and time, Detector efficiency and Dead time. Reference Books: 1. Marmier P. and Sheldon E., Physics of Nuclear & Particles, Vol.I & II 2. Lee S.Y., Accelerator Physics. 3. Persico E., Ferrari E, Sergre S. E., Principles of Particle Accelerators. 4. Green D, Principles of Particle Detector. 5. Knoll G. F., Radiation detection and measurement. 6. Burcham E., Nuclear & Particle Physics. 7. Ponearu D N and Greiner W, Experimental Techniques in Nuclear Physics, Walter de Gruyter Berlin, (1997) PY 2132 ELECTRONICS LAB [Minimum 10 experiments to be performed] 1. Design of a regulated power supply 2. Design of a common emitter transistor amplifier 3. Design of a stable multivibrator 4. Design of monostable and Design of Bistable multivibrators 5. SCR Characteristics 6. Wein bridge Oscillator 7. Phase shift oscillator 8. Zener diode charecteristics and voltage regulation. 9. FET and MOSFET characteristics and application as an amplifier. 10. LOGIC GATES: TTL, NAND and NOR gates 11. Digital II: Combinational Logic. FLIP-FLOPS 12. Operational Amplifiers (741). 13. Differential amplifier [0 0 8 4] 14. Experiment with Microprocessor kit PY 2431 Nuclear Physics Lab [0 0 8 4] 1. Dead time of GM tube by single source method and by double source method 2. Range of B particles using GM counter 3. Range and energy of Alpha particles by GM method 4. Inverse square law for Gamma radiation using GM Counter 5. Linear attenuation coefficient for γ- rays (GM). 6. Absorption of gamma rays by lead-mass absorption coefficient and half value thickness of the absorber . 7. Absorption coefficient by equivalent thickness method using GM detector 8. Characteristics of scintillation counter 9. To determine the operating voltage if a –photomultiplier tube and to find the Photo-peak efficiency of a Nal (Tl) crystal of given dimensions for gamma rays of different energies. 10. Statistics of counting [ using G. M Counter ] 11. To determine the energy resolution of a Nal(Tl) detector and to show that it is independent of the again of the amplifier. Self Study course III Semester PY 2111 MATHEMATICAL PHYSICS [3 1 0 4] Integral Transforms and Fourier transformations: Fourier series – Dirichlet’s conditions – Fourier series of even and odd functions Complex form of Fourier series – Fourier integral and it’s complex form – Fourier transforms – Fourier sine and cosine transforms – Convolution theorem and Parseval’s identity. Laplace transform of elementary functions – Inverse Laplace transforms .Methods of finding Inverse Laplace transforms – Heaviside expansion formula. Solutions of simple differential equations Curvilinear coordinates, Matrices: Generalized coordinates - elements of curvilinear coordinates - transformation of coordinates - orthogonal curvilinear coordinates - unit vectors - expression for arc length, volume element. The gradient, divergence and curl in orthogonal curvilinear coordinates. Laplacian in orthogonal curvilinear coordinates, spherical polar coordinates, cylindrical coordinates. Matrix representation of linear operators, Hermitian and unitary Solution of system of linear equations – coordinate transformation. Complex variables and integral transforms: Review of functions of a complex variable – Cauchy Riemann conditions. Contour integrals. Cauchy integral theorem, Cauchy integral formula. Taylor and Laurentz series. Zero isolated singular points, simple pole, mth order pole. Evaluation of residues. The Cauchy’s residue theorem. The Cauchy principle value. Evaluation of different forms of definite integrals. Tensor analysis and group theory: Introduction - rank of a tensor. Transformation of coordinates in linear spaces transformation law for the components of a second rank tensor. Contravarient and covariant and mixed tensors - First rank tensor, higher rank tensors, symmetric and antisymmetric tensors. Tensor algebra - outer product - contraction - inner product - quotient law. The fundamental metric tensor - associate tensors. Groups - subgroups - classes. Invarient subgroups - factor groups. Homomorphism and Isomorphism. Group representation - reducible and irreducible representation. Schur’s lemmas, orthogonality theorem. Decomposing reducible representation into irreducible ones. Construction of representations. Representation of groups and quantum mechanics. Lie groups and Lie algebra. Three dimensional rotation group SO(3), SU(2) and SU(3) groups. Special functions: Delta function and eview of power series method for ordinary differential equations description of beta and gamma functions. Bessel functions – solution of Bessel’s equation Neumann and Hankel functions – generating function and recurrence relations orthogonality of Bessel functions – Spherical Bessel functions. Legendre polynomials solution of Legendre equation – generating function and recurrence relations orthogonality property of Legendre polynomials – associated Legendre polynomials and spherical harmonics. Solution of Laguerre’s equation – Laguerre and associated Laguerre polynomials – Solution of Hermite equation – Hermite polynomials – generating functions and recurrence relations. Text and Reference Books: 1. Arfken G., Mathematical Methods for Physics, 4th edn., Academic press. 2. Joshi A. W., Matrices and Tensors for Physicists, Wiley Eastern. 3. Kreyzing E., Advanced Engineering Mathematics. 4. Rainville E. D., Special Functions. 5. Bell W. W., Special Functions. 6. Reily K. F. , Hobson M. P. and Bence S. J., Mathematical Methods for Physics and Engineering. 7. Boas M., Mathematics for Physics. 8. Churchill & Brown, Complex variables and applications,5th edn., McGrawHill. 9. Tung, Group theory in physics, World Scientific. 10. Ghatak et al, Mathematical physics, Macmillan. 11. Harper, Mathematical methods, PHI. Self Study course IV Semester PY 2211 . CLASSICAL ELECTRODYNAMICS [3 1 0 4] Electrostatics: Electric field: Gauss law, scalar potential, surface distribution of charges and dipoles and discontinuities in the electric field and potential, Poisson and-Laplace equations, Green's Theorem, Uniqueness of the solution with Dirichlet or Neumann Boundary Formal so1ution of Electrostatic Boundary value problem with conditions, Green's Function, Electrostatic potential energy and energy density, capacitance. Boundary- Value Problems in Electrostatics: Methods of Images, Point charge in the presence of a grounded conducting sphere point charge in the presence of a charge insulated conducting sphere, Point charge near a conducting sphere at fixed potential, conducting sphere in a uniform electric field by method of images, Green function for the sphere, General solution for the potential, Conducting sphere with Hemispheres at different potential, orthogonal functions and expansion. Magnetostatics: Biot, and Savart law, the differential equation of magnetostatics and Ampere's law, Vector potential and Magnetic induction for a circular current loop, Magnetic fields of a localized current distribution, Magnetic moment, Force and torque on and energy of a localized current distribution in an external magnetic induction, Macroscopic equations.Boundary conditions on B and H. Methods of solving Boundary-value problems in magneto statics, Uniformly magnetized sphere, Magnetized sphere in an external field, Permanent magnets, Magnetic shielding, spherical shell of permeable material in an uniform field. Multipoles, Electrostatics of Macroscopic Media Dielectrics: Multipole expansion, multipole expansion of the energy of a charge distribution in an external field, Elementary treatment of electrostatics with permeable media, Boundary value problems with dielectrics. Molar polarizability, and electric susceptibility. Models for molecular polarizability, Electro-static energy in dielectric media. Time varying fields, Maxwell's equations Conservation Laws: Energy in a magnetic field, Vector and Scalar potentials. Gauge transformations, Lorentz gauge, Coulomb gauge, Green functions for the wave equation, Derivation of the equations of Macroscopic Electromagnetism, Poyntings theorem and conservations of energy and momentum for a system of charged particles. Conservation laws for macroscopic media. Electromagnetic field tensor. Transformation of four, potentials and four currents. Tensor description of Maxwell's equation. Plane Electromagnetic Waves and Wave Equation: Plane wave in a nonconducting medium. Frequency dispersion characteristics of dielecttics, conductors and plasmas, waves in a conducting or dissipative medium, superposition of waves in one dimension, group velocity, casualty connection between D and E. KramersKroning relation. . Reference Books: 1. Jackson J.D., Classical Electrodynamics. 2. Panofsky and Philips, Classical Electricity and Magnetism. . 3. Griffiths, Introduction to Electrodynamics. 4. Landau and Lifshitz, Classical Theory of Field. 5. Landau and Lifshitz, Electrodynamics of Continuous Media. 6. Reitz and Milford, Foundations of electromagnetic theory, Addison Wesley.