University of Lucknow Courses

M.Sc. (Physics)

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Duration: 2 Years

Eligibility: Graduation

Course Structure

Semester - I

• Module 01 : Mathematical Physics-I
• Module 02 : Classical Mechanics
• Module 03 : Electromagnetic Theory
• Module 04 : Introductory Quantum Mechanics
• Module 05 : Practical
• Module 10 : Practical

Semester - II

• Module 06 : Mathematical Physics-II
• Module 07 : Statistical Mechanics
• Module 08 : Classical Electrodynamics
• Module 09 : Atomic And Molecular Spectra

Semester - III

• Module 11 : Quantum Mechanics-I
• Module 12 : Nuclear Physics - I
• Module 13 : Solid State Physics - I
• Module 14 : Electronics-I
• Module 15 : Electronics II
• Module 16 : Lasers And Opto-Electronics - I
• Module 17 : Lasers And Opto-Electronics - II
• Module 18 : X-Rays - I
• Module 19 : X-Rays - II

Semester - IV

• Module 20 : Quantum Mechanics - II
• Module 21 : Nuclear Physics - II
• Module 22 : Solid State Physics - II
• Module 23 : Electronics III
• Module 24 : Electronics Iv
• Module 25 : Lasers And Opto-Electronics - III
• Module 26 : Lasers And Opto-Electronics - Iv
• Module 27 : X-Rays - III
• Module 28 : X-Rays - IV

Practicals

• Module 29 : General Experiments
• Module 30 : Electronics Experiments
• Module 31 : Lasers & Opto-Electronics Experiments
• Module 32 : X-Ray Experiments

 

Note: Electronics, Lasers & Opto-electronics and X-Rays in Semesters III & IV are specializations. One specialization has to be opted by the student from the start of Semester III.

 

Course Detail

Semester - I

Module 01: Mathematical Physics-I

Unit - I

Fundamental laws of Algebra on complex numbers, polar form of complex numbers, Regions in the complex plane, Analytic (regular) functions, The Cauchy-Riemann equations, Harmonic functions.

Unit – II

Line integral in complex plane, Cauchy’s theorem, Cauchy’s integral formula, Taylor’s and Laurent’s expansions, singularities, Zeroes and poles, Residue theorem and count our integration of simple functions.

Unit – III

Power series, solution of second order differential equations, ordinary point and singularities of a linear differential equation, Solutions of Hyper- geometric, Bessel, Legendre, Laguerre and Hermite equations.

Unit – IV

Bessel and Legendre functions and polynomials, Rodrigue’s formula for Legendre polynomial Orthonrmality and other properties of Legendre, Associated Legendre, Hermit, Laguerre and Associated Lagurre polynomials.

 

Module 02: Classical Mechanics

Unit - I

Mechanics of a system of particles, Generalized Co ordinates, D Alembert’s principle. The Lagrangian formulation and equations of motion ( with full derivation). The Hamiltonian formulation and equations of motion ( with full derivation).

Unit – II

Calculus of variations and its application – Hamilton’s principle. The modified Hamilton’s principle and principle of least action, The rigid body motion – Euler angles, Motion of symmetrical top.

Unit – III

Canonical transformations, Poisson brackets, Equations of motion and infinitesimal  canonical transformations in the Poisson bracket formulation, Liouville’s theorem.

Unit – IV

Hamilton – Jacobi equations, Action angle variables, the connection between Hamilton- Jacobi theory and geometrical optics, Theory of small oscillations – Free vibrations of linear tri- atomic molecule, Transition from a discrete to a continuous system, Field equation-The Klein Gordan Equation.

 

Module 03: Electromagnetic Theory

Unit - I

Maxwell’s Equations in vacuum and matter, Maxwell’s correction to Ampere’s law for  non- steady currents and concept of Displacement current; Boundary conditions, Poynting’s theorem, Conservation of Energy and momentum for a system of charged particles and electromagnetic field.

Unit – II

Vactor and scalar potentials, Maxwell’s Equations in terms of Electromagnetic Potentials, Electromagnetic wave equation, Non-uniqueness of Electromagnetic Potentials and Concept of Gauge. Gauge Transformations: Coulomb and Lorentz Gauge; Green’s Function for the Wave Equation; Transformation Properties of Electromagnetic Fields and Sources under Rotation, Spatial Reflection and Time- Reversal.

Unit – III

Propagation of Electromagnetic Plane Waves in Vacuum, Non-conducting Medium, Conducting Medium and Plasma; Reflection, Refraction and Polarization of Electromagnetic Waves, Stokes Parameters; Frequency Dispersion Characteristics of Dielectrics and Conductors; Normal and Anomalous Dispersion, Spreading of Pulse in Dispersive Media, Kramer-Kronig Relations.

Unit – IV

Propagation of Electromagnetic Waves in Rectangular Waveguides, TE and TM Modes, Cut off frequency, Energy Flow and Attenuation. Modal Analysis of guided modes in a cylindrical waveguide. Field and Radiation due to an Oscillating Electric Dipole. Magnetic dipole and electric quadrupole fields.

 

Module 04: Introductory Quantum Mechanics

Unit - I

Coordinate and momentum representation, Hermitian operators and their spectrum, Commutator algebra, Uncertainty relation, Eigen values and eigen functions of Linear harmonic oscillator.

Unit – II

Motion in a central field, Hydrogen atom problem, Free particle in three dimensions, Eigen values and eigen functions of angular momentum operators L and Lz, spherical harmonics, Angular momentum commutation relations, Coupling of two angular momentum.

Unit – III

WKBJ approximation method, Rayleigh-Schrodinger time-independent perturbation theory for non-degenerate and degenerate systems, Anharmonic oscillator.

Unit – IV

Zeeman Effect, Normal and anomalous Zeeman effect of one electron system, Calculation of Zeeman patterns, First order Stark effect.

 

Module 05: PracticaL

General Electronics Experiments

• Single Stage Amplifier
• Zener Diode
• S.C.R.
• Ic Regulated Power Supply
• Negative Feed Back
• Modulation & Delodulation
• P-N Junction

 

Module 10: PracticaL

Optics & General Experiments

• Michelson Interferometer
• Etalon
• Grating
• Rayleigh
• olarization
• Edser-Butler
• Babinet Compensator
• Ultrasonic Interferometer
• Hystersis Loop Tracer

 

Semester - II

Module 06: Mathematical Physics-II

Unit - I

Partial differential equations, Lagrange’s linear equation, Method of multipliers, Solutions of Laplace, Poisson, Diffusion and wave equations.

Unit – II

Inhomogeneous equations, Green’s function for a free particle, Fourier series, Fourier integral, Fourier sine, cosine and complex transforms, Applications to boundary value problems, Fundamental properties of Beta and Gamma functions.

Unit – III

Binary operation, Definitions of Group, Semi-Group and Abelian group, Multiplication table, Equivalence class, Conjugate elements and classes, Invariant subgroups, Permutation group, Cyclic group, Cosets of a subgroup, finite and infinite group, Period of the group.

Unit – IV

Similarity transformations, Representation Character of Trace of the group, Schur’s Lemma and the Orthgonality theorem, Examples of C2v, Regular representation, Symmetriesed basis functions for irreducible representation, Direct product of representation. Applications to simple vibrational problems.

 

Module07: Statistical Mechanics

Unit I

Quantum statistics of identical particles, Symmetry properties, Postulates of equal a prior probability, Grand Canonical Ensemble, Quantum distribution functions (Bose- Einstein and Fermi-Dirac), Deviation of distribution laws using grand canonical partition function.

Unit II

Degeneracy of Boson gas, Applications of Bose-Einstein statistics, Bose-Einstein condensation, Planck’s Radiation law, properties of liquid He II, Derivation of energy and pressure of Fermi gas, Energy and pressure of Fermi gas at absolute zero, Fermi energy as a function of temperature, Thermodynamic properties of an electron gas.

Unit III

Gibbs Paradox, Phase transition, Gibb’s phase rule, One dimensional Ising model, Law of atmosphere, White Dwarf and Chandra Shekhar limit, Fluctuations, Energy fluctuations in canonical ensemble and concentration fluctuations in grand canonical ensemble.

Unit IV

Nyquist theorem (derivation and its applications), Thermodynamics of irreversible processes, Onsager reciprocal relations Phenomenological coefficient, Principle of minimum entropy production.

 

Module 08: Classical Electrodynamics

Unit - I

Homogeneous and inhomogeneous Lorentz groups, Spacetime rotations, rapidity, Proper, improper, orthochronous, antichronous Lorentz groups, Light cone interpretation of Lorentz transformations, Four-vectors, orthogonality, Four-tensors, Jacobians, Contravariant and Covariant tensors, Trace of a tensor, Contraction, Symmetric and Antisymmetric tensors, Inner and outer products, Quotient Law, Metric tensor, Pseudotensors, completely antisymmetric unit tensor, Four-velocity, fourmomentum, four-acceleration, Minkowski force.

Unit – II

2-Form electromagnetic field strength tensor, Covariant formulation of Maxwell’s field equations with gauge invariance, Lorentz force equation in covariant form, Transformation of electromagnetic fields as tensor components, Invariants of the field, Canonical approach to electrodynamics, Lagrangian and Hamiltonian formulation for a relativistic charged particle in external electromagnetic field, Canonical and Symmetric Stress Tensors, Conservation laws, Solution of the wave equation in covariant form, Invariant Green function.

Unit – III

Retarded and advanced potentials, Lienard-Wiechert potentials for a moving point charge, Fields produced by a charge in uniform and accelerated motion, Radiated power, Larmor’s formula and its relativistic generalization, Angular distribution of radiation due to an accelerated charge, bremsstrahlung, synchrotron radiation, Thomson scattering of radiation, Thomson cross section, Multipole expansion of electromagnetic fields, Properties of multipole fields, Energy and Angular momentum of multipole radiation.

Unit – IV

Radiation damping, Radiative reaction force and its derivation, Difficulties with classical Abraham-Lorentz model, Integro-differential equation of motion, Preacceleration,  Line breadth and Level shift of an oscillator, Scattering by free and bound electrons, Rayleigh Scattering, Frequency dependence of total cross section, Resonance fluorescence.

 

Module 09: Atomic and Molecular Spectra

Unit – I

Fine structure of Hydrogen lines, Optical spectra of alkali metals, Paschen-Back effect of one electron system, Optical spectra of alkaline earth elements, Singlet and triplet terms.

Unit – II

Coupling scheme for two electron systems, Hund’s rule. Hyperfine structure, Isotope effect in atomic spectra, distinction between Isotope effect and hyperfine structure, Lande’s interval rule, Lamb Rutherford Shift.

Unit – III

Rotation and Rotation- Vibration spectra of diatomic molecules, Microwave and Infrared absorption, Raman scattering, Selection rules, P.Q and R branches, Isotopic shift, Determination of heat of dissociation, Effect of anharmonicity, Coriolis force

Unit – IV

Vibronic-transition and Frank-Condon rule, principle of Lasers (He-Ne gas laser, ruby laser) and uses of lasers in Raman spectroscopy, Principle of E.S.R, N.M.R, and N.Q.R. spectroscopy.

 

Semester - III

Module 11: Quantum Mechanics - I

Unit – I

Matrix formulation of Quantum Mechanics- Transformation theory, Hilbert space and Projection operators. Equations of motion in Schrödinger, Heisenberg and Interaction pictures. Harmonic oscillator.

Unit – II

Symmetry in Quantum Mechanics- Space and time development, Rotation and angular momentum, Angular and spin momentum matrices, Combination of angular momenta. Tensor operators. Space inversion and time Reversal.

Unit – III

Variational Method, Time dependent perturbation theory. Classical theory of radiation, Transition probabilities, Einstein’s coefficients.  Identical particles with spin. Symmetry and Antisymmetry of wave functions, Slater’s determinantal wave functions. Excited states of Helium atom.

Unit – IV

Non-relativistic scattering theory: Born approximation method with examples of scattering by Coulomb, Gaussian, Square well and Yukawa potential. Partial wave analysis, phase shift, example of square well potentials. Scattering by identical particles (expression for scattering cross-section only) Atomic scattering of fast electrons.

 

Module 12: Nuclear Physics - I

Unit – I

Basic facts about nuclei, Mass and binding energy, Semi-empirical mass formula, Nuclear size determination using mu-mesic X-rays and scattering of fast electrons, Nuclear spin and magnetic moment of nuclei, Molecular beam resonance method, Nuclear resonance absorption and induction method, Electric quadrupole moment

Unit – II

Alpha decay, Experimental results on alpha decay-Alpha spectra and Geiger- Nutall relation, Theory of alpha decay. Beta-spectra, Fermi’s theory of beta decay, Sergeant’s law, Kurie Plot, Allowed and forbidden transitions, Parity violation in beta-decay, Detection of neutrino.

Unit III

Gamma emission, Multipolarity of gamma rays, Selection rules, Theoretical prediction of decay constants, Estimation of Transition probabilities, Internal conversion, Angular correlation, Nuclear isomerism, Mossbauer Effect.

Unit – IV

Nuclear reactions, Conservation laws, The Q-equation and deduction of nuclear energy levels, Compound nucleus, Bohr hypothesis, Resonance phenomena, Breit- Wigner one level formula, Optical model, Simple discussion of direct reactions, Nuclear fission, Bohr-Wheeler theory of nuclear fission, Controlled chain reaction, Nuclear reactors, Nuclear Fusion.

 

Module 13: Solid State Physics - I

Unit -  I

Lattice Dynamics – Phonon dispersion spectra for three dimensional monatomic solids, Density of states, Phonon branches in 3-d solid with a polyatomic basis, Local phonon modes. Inelastic scattering by phonons, Experimental measurements of phonons, Phonon heat capacity, Debye model and Born cut-off procedure, Thermal conduction: lattice thermal conduction and phonon free path, anharmonic effects. Normal and umklapp process, defect controlled phonon scattering, Heat capacity of amorphous material.

Unit - II

Free Electron Theory- Electrical conductivity, Sommerfeld’s; Wiedmann-Franz law, Lorentz number, Motion in magnetic fields, Plasmons, Plasma optics, Dispersion relation for electromagnetic waves, Transverse and longitudinal modes, transparency of alkali halide crystals in ultraviolet light, Screening effect, Mott metal-insulator transitor, Polaritons, Electron-electron interaction, Electron-phonon interaction, Polarons.

Unit - III

Semi-conductors- Lattice properties of 4th group elements: Structure, physical constants, influence of impurities, diffusion of impurities, Influence of lattice defects, Fermi level and electron-hole distribution in energy bands, Models of an impurity semiconductor, Temperature dependence of Fermi level in an extrinsic semi-conductor, Conductivity and Hall effect in semi-conductors, Constant energy surfaces and effective mass in Si and Ge, Effect of temperature and impurties in semi-conductors, Rectification, Schottky barrier, Heterostructures. N-N heterojunction. semi-conductor, Introduction to amorphous semi-conductors.

Unit - IV

Superconductivity- Concept of superconductivity, Meissner effect, Type I and type II superconductors, Energy gap, Isotope Effect, Microwave and infrared properties, London equations, Penetration depth, Coherence length, Super-conductivity ground state, BCS theory, Flux quantization in a ring, Electron tunneling. DC & AC Josephson Effect, Macroscopic quantum interference. SQUID, Introduction to high Tc superconductors.

Dislocation in Solids- Dislocation stress and strain, Fields of dislocations, Dislocation multiplication.

 

Module 14: Electronics-I

Unit -  I Linear Wave Shaping

High Pass and Low Pass RC Networks, Response to Sinusoidal, Step, Pulse, Square wave, Exponential and Ramp Inputs. High pass RC circuit as a differentiator, Criterion for good differentiation, Double Differentiation, Low Pass RC circuit as an Integrator. Laplace Transforms and their application to circuit elements.

Unit -  II Amplifiers

Difference Amplifiers, Broadband Amplifiers, Methods for achieving Broadbanding, Emitter Follower at High Frequencies, Operational Amplifiers and its Applications, IC 741, Active Filters.

Unit - III Power Supplies

Electronically Regulated Power Supplies, Converters and Inverters, High and Low Voltage Supplies, Application of SCR as Regulator, SMPS.

Unit - IV: Integrated Circuit Fabrication Technology

Basic Monolithic Integrated Circuits, Steps involved in the Manufacture of Monolithic ICs: Epitaxy, Masking, Etching, Diffusion, Metallization, Bonding, Assembling, Package types. Introduction to VLSI techniques.

 

Module 15: Electronics II

Unit  - I Logic Hardware

Transistor as a Switch, Switching times: Definition and Derivation: Rise Time, Fall Time, Storage Time, Delay Time, Turn On Time, Turn Off Time, Charge Control Analysis. Logic Specifications: Fan In, Fan Out, Noise Immunity, Noise Margin, Propagation Delay, Power Dissipation. Logic Families: DTL, DC TL, I2L, ECL, TTL, CMOSL, CML, HTL.

Unit  - II: Number Systems and Boolean Algebra

Binary, Octal and Hexadecimal Number Systems. Binary Arithmetic. Arithmetic Circuits. Binary Codes: Gray, 8421, 2421, 5211. Boolean Variables and Operators, Simplification of Boolean Expressions. Karnaugh Maps.

Unit - III Multivibrators

Astable, Monostable and Bistable Multivibrators. Schmitt Trigger. 555 Timer. RS, RST, JK, T, D, JK M/S Flip flops, Race problem, Preset and Clear Functions.

Unit  - IV Counters and Registers

Binary Counters: Up, Down, Parallel. Modulus Counters: Counter Reset Method, Logic Gating Method. Ring Counter. Shift Registers: SISO, PIPO, SIPO, PISO. Universal Shift Register. Tristate Switches, Tristate Registers.

 

Module 16: Lasers and Opto-Electronics - I

Unit - I

Laser theory, Einstein Coefficients, Light Amplification, threshold condition, Laser Rate Equations-two, three and four level systems.

Unit - II

Laser power around threshold, optimum output coupling, Line Broadening Mechanisms – Natural, Collision and Doppler, Optical Resonators – Modes of a rectangular cavity and open planar resonator, Modes of a Confocal resonator system, General Spherical resonator, Higher order modes.

Unit - III

Essential criterion to observe non linear optical effects. First experimental demonstration of non-linear phenomena. Classical theory of non-linear response in one dimension. Generalization to 3 dimensions. General properties of the polarizability tensor – Reality condition, Intrinsic symmetry, general form and frequency dependence, overall symmetry. Second harmonic generation and phase matching techniques. Basic idea of self-focusing.

Unit - IV

Non-linear coupling of 3 waves to produce sum and difference frequencies. Manley Rowe relations and their significance. Sum and difference frequency generation when both input frequencies are lasers. Parametric conversion and amplification. Basic idea of optical phase conjugation.

 

Module 17: Lasers and Opto-Electronics - II

Unit I

Optical sources: Direct and Indirect Band Gap materials, Light source Material Heterojunction structure. Surface Emitting and Edge Emitting LED Quantum Efficiency, Modulation Capability, analog & Digital Modulation, Laser Diode, Modes and Threshold Condition, Resonant frequencies, Radiation pattern, Modulation of LD, Temperature Effect, Modal, Partition and Reflection Noise, Advantages of LD over LED. Wave length window regions, Basic idea of Quantum dot, Quantum wire Laser and VCSELs.

Unit - II

Photo Detectors: Principle of operation, Performance parameters, Quantum efficiency, Responsibility, Cut off wave length, Photo detector Material. Frequency Response, Thermal Noise, Shot-Noise Signal to noise ratio, NEP (Noise Equivalent Power) structure of PIN and APD, Equivalent Circuit, Temperature effect on Avalanche gain, CCD, LED and LCD display.

Unit - III

Fiber as a guiding medium, Total Internal reflection Acceptance angle Numerical aperture, types of fiber, Refractive index profiles, Concept of modes, Electromagnetic analysis of guided modes in symmetric step index planar wave guide and step index fiber.

Unit - IV

Concept of Normalized Frequency, V Parameter, Pulse dispersion in step index fibers. Concept of Dispersion shifted and Dispersion flattened Fibers, Fiber attenuation, Misalignment losses, Fiber material, Fiber fabrication, Splices & Connectors.

 

Module 18: X-Rays - I

Unit - I

Scattering of X-rays, Compton scattering and Thompson’s theory scattering by a pair of electrons and electron cloud in an atom, Atomic structure factors.

Unit - II

Scattering by diatomic and simple polyatomic molecules, Scattering by liquids and determination of atomic distribution in monatomic liquids, Zernicks Prins Formula.

Unit - III

Diffraction of x-rays by Crystals, Laue’s and Bragg’s equations for X-ray diffraction and their equivalency , Reciprocal lattice, Neutron and electron diffraction, relative merits and demerits of electron ,neutron and X-ray diffraction, point groups and Space groups.

Unit - IV

Various methods of X-ray diffraction; Collimation and recording of X-ray beam, Laue, Powder, Rotating/oscillating and moving film methods in details. Interpretation of diffraction pattern with the help of various tools, factors affecting X-ray intensities.

 

Module 19: X-rays - II

Unit - I

Production and detection of X-rays, X-ray tubes, Problems in tube design, High Tension equipments, Ionization Detections methods, X-ray spectrographs and spectrometers: Single crystal, Double crystal and Bent crystal spectrographic and their resolving powers.

Unit - II

X-ray emission from thin and thick targets, Theories of continuous X-ray spectra: Sommerfeld’s theory for the spectral distribution frequency spectrum of continuous Xray Experimental spectral and spatial distribution, shortcomings of classical theory, kramers quantum theory

Unit  - III

X-ray emission spectra, X-ray energy level diagram, multiple transitions Selection rules,  Spin and Screening doublets, screening parameters and their determination, X-ray satellites and their origin: Wetzel-Drwyvesteyn theory of high energy satellites, theories for low energy satellites.

Unit  - IV

Rearrangement of atomic electrons following inner shell loisation, Radiative transitions, Auger effect and its consequences in X-ray spectra, Coster-Kronig transitions, the super coster-Kronig transitions, Fluorescence yield, Auto ionization and internal conversion.

Semester - IV 

Module 20: Quantum Mechanics - II

Unit – I

Thomas-Fermi model. Self-consistent fields, Hartee-Fock Theory. Heitler-London Theory of hydrogen molecule, Ortho and para Hydrogen. Bonding and Anti-bonding orbitals. Valence bond theory, Molecular orbitals. LCAO method.

Unit – II

Relativistic Wave Equations – Klein-Gordon equation, Dirac equation: formulation, covariant form, proof of covariance, space reflection. Free particle solution and nonrelativistic reduction. Projection operators for energy and spin. Negative energy states: Zitterbewegung, hole theory. Central force problems: Hydrogen atom, spin orbit energy, magnetic moment.

Unit – III

Definition of Hamiltonian and Lagrangian for fields. Second quantization of Klein- Gordon, Schrodinger and Dirac equations. Creation, annihilation and number operators.

Unit – IV

Quantization of radiation field. Absorption, induced and spontaneous emission. Transition probabilities. Planck’s formula.

 

Module 21: Nuclear Physics - II

Unit - I

Nuclear two-body problem, Simple theory of deuteron, Spin dependence and noncentral feature of nuclear forces, Partial wave analysis, Low energy n-p scattering, Scattering length and effective range theory, Low energy p-p scattering, Charge symmetry and charge independence of nuclear forces, Meson theory of nuclear forces.

Unit -  II

Nuclear models, Evidence of shell structure, magic numbers and spin-orbit coupling, extreme single particle model. Predictions of spin, parity and electromagnetic moments, Collective model-Vibrational and rotational spectra.

Unit  - III

Classification of elementary particles, Exact conservation laws, Approximate conservation laws: isospin and isospin wave functions for pion-nucleon system, strangeness, parity, time reversal and charge conjugation, CP violation.

Unit- IV

Eight fold way, Quarks, Quark-Quark interaction, SU (3) quark model, Magnetic dipole moment of baryons, Masses of hadrons, Basic ideas about the standard model.

 

Module 22: Solid State Physics - II

Unit - I

Dielectric and Ferroelectric Properties- Macroscopic electric field, Local field at an atom, Clausius-Mosotti equation, Dielectric constant and polarisability, Electronic Polarisability, Classical theory of electronic polarisability, Structural phase transition, Soft modes, Antiferroelectricity, Ferroelectric domains, Piezoelectricity.

Unit -  II

Magnetic properties- Quantum theory of diamagnetism and paramagnetism, Susceptibility behaviour of paramagnetic systems, super paramagnetism, Behaviour of Fe and rare earth groups, Quenching of oribital magnetic moments, paramagnetic moment of metallic solids. Van Vleck paramagnetism, Heisenberg theory, Spin wave theory for ferromagnetic and antiferromagnetic systems, T3/2 law. Acoustic and optical magnons, Phase transformation in antiferromagnetic systems, Susceptibility behaviour of ordered systems, Anisotropy. Domain theory, Bloch wall, Coercivity and Hysterisis. Amorphous ferromagnets.

Unit - III

Band Theory- Bloch theorem, Tight binding approximatin, LCAO method and its application, derivation of dispersion relation, concepts of effective mass and holes, Brillouin zones, reduced zone scheme, Shape of bands and their overlapping, Behaviour of ionic-covalent and metallic solids. Construction of Fermi-surfaces, Methods for the study of Fermisurfaces, Anomalous Skin Effect, Cyclotron resonance, Extremal orbits, Landau energy levels, Magnetic subbands, Landau diamagnetism, de Hass-van Alphen Effect, Shubnikov-de Hass effect, Quantum Hall Effect.

Unit - IV

Electronic and optical properties- The upper filled band and the conduction band in ionic crystals, Excitons, Qualitative discussion of lattice defects and their influence on electronic levels, Colour centers, Luminescence, thallium activated alkali halides.

General – Alloys: Substitutional solid solution, Order disorder transformation, Phase diagrams, Elementary theory of order, Transition metal alloys and KONDO effects.

 

Module 23: Electronics III

Unit - I Amplitude Modulation

Amplitude Modulation, Spectrum of the modulated signal, Square law Modulator, Balanced Modulator, DSBSC, SSB and vestigial sideband modulation. Limitations of Amplitude Modulation.

Unit  - II Frequency Modulation

Analysis and frequency Spectrum, Generation and Detection of FM. Comparison of AM and FM. Pre-emphasis and De-emphasis. Reactance Modulator. Capture Effect. Varactor Modulator. Amplitude Limiter. FM Receiver. Foster Seely Discriminator. Ratio Detector.

Unit - III Television

TV Camera tubes, Image Orthicon, Vidicon, Plumbicon. Interlaced Scanning. Transmitter/Receiver. Synchronization. Resolution. TV Signal. Vestigial Sideband Modulation. B/W TV Receiver Block Diagram. Sync. Separator. Vertical and Horizontal deflection circuits. Principles of Colour TV. Chroma Modulation. Colour Picture Tube.

Unit - IV Digital Communication:

Digital Line Waveforms: Symbols, Bits and Bauds . Functional Notation for Pulses, Line Codes and Waveforms. M-ary encoding. Pulse Modulation: Pulse Amplitude, Pulse Code, Pulse Frequency, Pulse Time, Pulse Position and Pulse Width Modulation. Differential PCM, Delta Modulation. Digital Communication System. Digital Carrier System. Frequency Shift Keying. Phase Shift Keying. Differential Phase Shift Keying. Digital Multiplexing.

 

Module 24: Electronics IV

Unit - I Combinational Logic Circuits

• Pin out Diagrams, Truth Tables, Working.
• Decoders: 1-of-4 IC 74AS139, 1-of-16 IC 74154
• BCD to Decimal Decoder IC 7445, BCD to Seven Segment Decoder Driver: IC 7447A, 7448.
• Encoders: Decimal Priority Encoder IC 74147
• Multiplexers: IC 74151, Implememtation of Boolean Function
• Demultiplexers: 1-of-16 Demultiplexer/ Decoder.

Unit - II Memories

• Memory Devices: Read Only Memories, Masked Memory, ROM, Programmable ROM, EPROM.
• Random Access Memory: Static and Dynamic, Bipolar Ram Cell, Static RAM cell.

Unit - III A/D and D/A Converters

• Weighted Resistor D/A Converter, Ladder Network D/A Converter. D/A Converter
• Specifications: Resolution, Accuracy, Linearity, Settling Time, Temperature Sensitivity.
• Flash A/D Converter, Ramp A/D Converter, Successive Approximation A/D Converter.

Unit -  IV Microprocessors and Displays:

LED Displays: Common Anode Display FND 507, FND 567.Common Cathode Display FND 500, FND 560. Flat Panel Displays(LCD, Plasmas etc.) and their addressing techniques. Smart Windows.

Intel Microprocessors: Historical Perspective. Organization of Microprocessor based system. 8085: Programming model. Registers, Accumulator, Flags, Program Counter, Stack Pointer. 8085 Instruction Set: Data Transfer Operation, Arithmetic Operations, Logic Operations, Branching Operations, One, Two and Three Byte Instructions, Opcode Format.

 

Module 25: Lasers and Opto-Electronics - III

Unit - I

Conventional versus holographic photography, Hologram of a point source, hologram of an extended object, Off-axis technique in the recording of holograms. Three dimensional holograms – Reflection holograms. Basic idea of holographic data storage, Holographic interferometry – double exposure, real time, time average holographic interferometry. Optical correlation. Fourier Transform holograms and their use in character recognition.

Unit - II

Optical data processing (basic idea). Abbe’s theory. Spatial filters – low pass, high pass, band pass filters. Fraunhofer Diffraction and the Fourier Transform – mathematical concept. Young’s experiment. Michelson Stellar interferometer and its limitation. Hanbury Brown and Twiss interferometer. Classical and quantum coherence functions, first and second order coherence, coherent states. Discussion of Young’s experiment in quantum mechanical terms.

Unit - III

Losses in the cavity – quality factor, line width of the Laser, Mode selection – Transverse and longitudinal, free spectral range and finesse of etalon, Q – Switching – Peak Power, Total Energy, Pulse duration, Techniques for Q- Switching- Mechanical, electro-optic and acousto-optic. Mode locking in lasers – Theory, Techniques for mode locking – Acousto-optic and electro-optic.

Unit - IV

Laser Systems – Ruby Laser, He-Ne Laser, Nd:YAG, Nd: Glass, CO2 Laser, Excimer Laser, Free Electron Lasers – Introduction, Single particle dynamics, wiggler, electron Trajectory, FEL Gain, Spontaneous Emission, effect of input wave polarization on FEL gain, Properties of Lasers – Directionality, Coherence etc.

 

Module 26: Lasers and Opto-Electronics - IV

Unit - I

Quantization of Analog signal, A/D & D/A conversion, Bit Rate, Pulse Code Modulation, NRZ, RZ and Manchester Coding, Base Line Wander Effect, Advantages of Optical Communication, Eye pattern Technique Time Division Multiplexing, Wave length Division Multiplexing WDM Devices, Multiplexers & De-Multiplexers.

Unit - II

Direct Detection and Coherent Heterodyne Detection concept of Optical frequency Division Multiplexing, NEP Heterodyne, Optical Amplifiers, Erbium Doped Fiber Amplifier, Semi Conductor Optical Amplifier, Fiber Bragg Grating, System Design, Power Budget, Band width Budget and Rise Time Budget Calculations.

Unit - III

Electromagnetic analysis of guided modes in symmetric step index planar waveguide. Basic idea of asymmetric planar waveguides. Basic idea of slab guide geometries: strip, raised strip, embedded strip, ridge, strip coated guides.  Beam and waveguide couplers: Transverse couplers, the prism-coupler, the Grating coupler, the thin-film tapered coupler, wave guide-to-fiber couplers.

Unit - IV

Electro-optic Effects, Acousto-optic Effect, Raman-Nath, Acousto-optic modulator, Bragg modulator, Acousto-optic deflectors, Acousto-optic spectrum analyzer.

Fabrication of Integrated optical Devices: Methods used to produce wave guiding layers, substrate preparation, cleaning of the substrate, Sputtering and Dipping, Ion migration. Idea of Remote Sensing.

Fiber optic sensors: Phase and polarization fiber sensors, Intrinsic sensors, Extrinsic fiber sensors, Gyroscope, Sagnac Effect etc.

 

Module 27: X-Rays - III

Unit - I

Derived charge distribution and a comparison with Hartee-Fock and Thomas-Fermi models, Intensity of scattering from free electrons. Klein Nisima formula (no derivation), Comparison with experiments.

Unit - II

Dispersion theory applied to x-rays, Anomalous dispersion, The forced, Damped oscillations of an electron and dielectric constant of the medium. Significance of complex dielectric constant. The index of refraction,experimental methods for measuring the refractive index.

Unit - III

Crystal structure factor calculation for fcc, bcc, hcp lattice, Space lattice extinction, Relative merits of crystal structure determination. The phase problem and various methods of its solution, trial and error methods, optical method, Fourier and Patterson methods.

Unit - IV

Small angle X-ray scattering (SAXS) from crystalline and non-crystalline materials; General theory; scattering by a single particle, group of particles. Experimental consideration for construction of SAXS apparatus, method of interpretation and comparison of experimental SAXS results and its application to the study of metals, alloys, polymers, finally dispersed solid, large molecules etc.

 

Module 28: X-Rays - IV

Unit - I:

X-ray absorption, Absorption coefficients, Characteristic absorption limits and  associated fine structure. Theory of absorption curve shape, Nature of the main absorption edge and the white line.

Unit - II:

Long Range Order and Short Range Order theories of X-ray absorption fine structure, Kronig theory, Hayasi modification of Kronig Theory Single and double potential model of Lytle. Chemical shifts in X-ray emission and absorption spectra.

Unit - III:

Soft X-ray spectroscopy, experimental methods and its use in the study of band structure of solids, Chemical analysis by X-ray emission, absorption and fluorescence spectroscopy.

Unit - IV: X-ray photoelectron spectroscopy, ESCA, its principle and applications in the study of solid surfaces, Auger electron spectroscopy and Appearance potential spectroscopy.

 

Practicals

Module 29:

General Experiments

• Hall Effect
• E.S.R.
• Four Probe
• Forbidden Energy Gap
• GM Counter
• β-Energy
• Klystron

 

Module 30:

Electronics Experiments

• Study of Digital Circuits.
• Study of Emitter Follower.
• Study of Difference Amplifier.
• Study of Schmitt Trigger.
• Study of PAM, PWM, PPM.
• Study of PCM Receiver and Transmitter.
• Study of OPAMP Characteristics.
• Study of OPAMP Applications.
• Study of Analog to Digital Converters.
• Study of Digital to Analog Converters.
• Study of Multivibrators.
• Study of 555 Timer.
• Study of ALU IC 74181.
• Study of Microprocessor IC 8085

 

Module 31:

Lasers & Opto-Electronics Experiments

• Study of characteristics of LED and PIN Photo Detector
• Study of frequency response of optical receiver
• To study attenuation in optical fibers
• To find numerical aperture of optical fibers
• Study of noise in an optical receiver
• To study Abbe’s Theory of image formation and spatial filtering
• To study diffraction pattern using a software controlled set-up
• Self-imaging
• To study microbending losses in an optical fiber
• Study of pulse amplitude modulation and time division multiplexing
• Study of Digital data communication
  

 

Module 32:

X-ray Experiments

• To take the powder photograph of Cu & W and index it
• To take the Laue photograph of KCl and index it
• To determine the wavelength of Kα & Kβ lines of Mo by means of Muller spectrograph
• To take the 15 degree oscillation photograph of KDP crystal and hence index the Reflection spot
• To take absorption spectra using bent crystal cauchois type spectrography