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SCHEME

M.Sc. (APPLIED PHYSICS) PART – I (I & II SEMESTER) 2017-2018 sessions

Code Title of Paper Hours (Per Week)

Max Marks ExaminationTime (Hours)

SEMESTER – I Total Ext. Int. TotalCore Papers

AP 1.1.1 Applied Mathematics 4 80 60 20 3

AP 1.1.2 Nuclear Science 4 80 60 20 3

AP 1.1.3 Classical Mechanics 4 80 60 20 3

Elective Papers*

AP 1.1.4 (i) Analog Electronics(ii) Remote Sensing(iii) Microwave and its

Propagation

4 80 60 20 3

AP 1.1.5 Laboratory Practice: i) Electronics Labii) Laser-Optics Lab

7 80 60 20 3

AP 1.1.6 Computer Laboratory 2 40 30 10 3

AP 1.1.7 Workshop (Mechanical/Optical) 5 60 45 15 3

SEMESTER – II

Core Papers

AP 1.2.1 Digital Electronics 4 80 60 20 3

AP 1.2.2 Radiation Physics 4 80 60 20 3

AP 1.2.3 Quantum Mechanics 4 80 60 20 3

Elective Papers*

AP 1.2.4 (i) Applied Optics (ii) Mathematical Physics and

Classical Mechanicsiii) Computer Fundamentals and

Programming with C++

4 80 60 20 3

AP 1.2.5 Laboratory Practice: i) Electronics Labii) Laser-Optics Lab

7 80 60 20 3

AP 1.2.6 Computer Laboratory 2 40 30 10 3

AP 1.2.7 Workshop(Mechanical/Optical) 5 60 45 15 3

For Other Departments Students: Qualifying Paper in Semester -IIPAPER: Domestic Use of Electric Gadgets

NOTE: Only one Elective paper will be offered depending on the availability of staff.*

Semester – I

AP 1.1.1 APPLIED MATHEMATICS

Maximum Marks: External 60 Time Allowed: 3 Hours Internal 20 Total Teaching hours: 50 Total 80 Pass Marks: 35%

Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examinations, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective section of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carries 10 marks. Section C will carry 20 marks.

Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks.

Use of scientific calculator is allowed.

SECTION AGamma and Beta functions: Definition and their relations

Bessel functions: Series solutions of Bessel's differential equation recurrence relations, Evaluation of Jn(x) for half-integral, generating function, Orthogonality (statement only). Legendre Polynomials: Series solution of Legendre differential equation, Rodrigue and recurrence formulae, Generating function; Associated Legendre equation and polynomials;

Hermite polynomials: Series solution of Hermite differential equation, Hermite polynomials, Generating functions, Recurrence relations, Orthogonality (statement only), Simple integral involving Hermite polynomials.

Laplace transforms: Definition, Laplace transform of elementary functions, Basic theorems of Laplace transforms, Inverse Laplace transforms, its properties and related theorems, Convolution theorem, Use of Laplace transforms in the solution of differential and integral equations, Evaluation of integrals using Laplace transforms.

Fourier series and transform: Dirichlet conditions, Expansion of periodic functions in Fourier series, Sine and cosine series, The finite Fourier sine and cosine transforms, Complex form of Fourier series, Fourier integral theorem and Fourier transform, Parseval's identity for Fourier series and transforms.

SECTION BPartial differential equations: One dimensional wave equation, The vibrating string fixed at both ends, D'Alembert and Fourier series solutions, Vibrations of a freely hanging chain, Two dimensional wave equation in rectangular membrane, Wave equation in the two dimensional polar coordinates and vibrations of a circular membrane, 3-D wave equation and its solution, Equation of heat conduction, Two dimensional heat conduction, Temperature distribution in a rectangular and circular plate, 3-D heat conduction equation.

Evaluation of polynomials: Horner's method; Root finding: Fixed point iteration, Bisection method, Regula falsi method, Newton method, Error analysis; System of linear equations: Gauss elimination, Gauss Seidel method, Interpolation and Extrapolation: Lagrange's interpolation, least square fitting; Differentiation and Integration: Difference operators, Simpson and trapezoidal rules; Ordinary differential equation: Euler method, Taylor method.

Text Books:1. Applied Mathematics: L.A. Pipes and Harwill, Mc Graw Hill Publication2. Mathematical Physics: G.R.Arfken, H.I.Weber, Academic Press, USA (Ind.Ed.)3. Laplace Transforms: M.R. Speigel (Schaum Series), Mc Graw Hill Publication4. Numerical Methods: J.H. Mathews, Prentice Hall of India, New Delhi

Text Books:1. Advanced Engg. Mathematics: E. Kreyszig, Wiley Eastern Publication.

AP 1.1.2 NUCLEAR SCIENCE






Section A

Nuclear Properties: Nuclear Radius, Mass and abundance of nuclides, Nuclear binding energy, Nuclear angular momentum and parity, Nuclear electromagnetic moments, Nuclear excited states, Nuclear forces and ground state properties of deuteron.

Nuclear Models: Liquid drop model, Shell model, even-Z even-N and collective structure, Many particle shell model and single particle states in deformed nucleus.

Nuclear decay processes: Alpha decay: Cause of alpha decay, basic alpha decay processes, alpha decay systematic, Theory of alpha emission. Angular momentum and parity in alpha decay.

Beta decay: Energy released in beta decay, Fermi theory of beta decay, Angular momentum and parity selection rules, forbidden decays, neutrino physics, non-conservation of parity in beta decay.

Gamma decay: Energies of gamma decay, Angular momentum and parity selection rules, transition probabilities and internal conversion process.

Section BSources of Nuclear RadiationNeutron Sources: Alpha particle neutron sources, photo neutron sources, Accelerators and nuclear reactors as sources of neutrons.

Sources of Charged Particles: Fast electron source, Heavy charged particle sources, Principle and working of different accelerators e.g. Tandem accelerator, Pelletron, Linear accelerator and Colliding beam accelerator.

Sources of Electromagnetic Radiation: Gamma rays following Beta decay and nuclear reactions, Annihilation radiations, Bremsstrahlung and characteristic X-rays.

Nuclear Reactions: Types of Nuclear Reactions and conservation laws, Energetics of nuclear reactions, Isospin, Reaction cross-section, Coulomb scattering, optical model, Compound nucleus reaction. Direct reaction, Resonance reaction. Heavy ion reaction, Fission and fusion.

Text Books:1. Introductory Nuclear Physics: K. S. Krane, Wiley & Sons, New Delhi.2. Elements of Nuclear Physics: W.E. Burcham, Longman Group Ltd.3. Nuclear Physics: I. Kaplan, Narosa Publishing House, New Delhi.4. The Atomic Nucleus: R. D. Evans, Tata Mc Graw Hill, New Delhi.5. Radiation Detection and Measurements: G. F. Knoll, Willy & Sons, New Delhi

AP 1.1.3 CLASSICAL MECHANICS





Use of scientific calculator is allowed..

Section A

Lagrangian Formulation: Conservation laws of linear momentum, angular momentum and energy for a single particle and system of particles, Constraints and generalized co-ordinates, Principle of virtual work, D' Alembert's principle and Lagrange's equations of motion, for conservative systems. Applications of Lagrangian formulation.

Variational Principle: Hamilton's principle, Calculus of variations and its application to the shortest distance, minimum surface area of revolution and the brachistochrone problem. Lagrange's equations from Hamilton's principle. Generalized momentum, Cyclic co-ordinates, Symmetry properties and Conservation theorems.

Two body Central Force Problem: Equivalent one body problem, Equations of motion and first integrals, Classification of orbits, Differential equation for the orbit, Kepler problem, Differential and total scattering cross-section, Scattering in an inverse square force field and Rutherford scattering cross section formula, Scattering in lab and center of mass frame.

Section B

Hamiltonian Formulation: Legendre transformation, Hamilton's equations of motion and their physical applications, Hamilton's equations from variational principle, Principle of least action.

Canonical Transformations: Point and canonical transformations, Generating functions, Poisson's brackets and its canonical invariance, Equations of motion in Poisson Bracket formulation, Poisson bracket relations between components of linear and angular momenta. Harmonic oscillator problem, check for transformation to be canonical and determination of generating functions.

Small Oscillations: Eigen value equation, Frequencies of free vibration and normal modes, Normal mode frequencies and eigen vectors of diatomic and linear tri-atomic molecule.

Rigid Body Motion: Orientation of a rigid body, Orthogonal transformations and properties of the orthogonal transformation matrix, Euler angles, Euler's theorem, Infinitesimal rotation, Rate of change of vector in rotating frame, Components of angular velocity along space and body set of axes. Motion of heavy symmetrical top (Analytical treatment).

Text Books:1. Classical Mechanics: H. Goldstein (Narosa Pub.)2. Classical Mechanics: J.C. Upadhyaya (Himalaya Pub. House)

AP 1.1.4 Elective Paper: Option (i) ANALOG ELECTRONICS






SECTION A

Two port network analysis: Active circuit model's equivalent circuit for BJT, Transconductance model: Common emitter. Common base. Common collector amplifiers. Equivalent circuit for FET. Common source amplifier. Source follower circuit (RR1)

Feedback in amplifiers: Stabilization of gain and reduction of non-linear distortion by negative feedback. Effect of feedback on input and output resistance. Voltage and current feedback (RR1)

Bias for transistor amplifier : Fixed bias circuit, Voltage feedback bias. Emitter feedback bias, Voltage divider bias method, Bias for FET (RR1)

Multistage amplifier : Direct coupled CE two stage amplifier. RC coupling and its analysis in mid- high-and low-frequency range. Effect of cascading on bandwidth. Darlington and cascade circuits (RR1)

Oscillators : Feedback and circuit requirements for oscillator, Basic oscillator analysis, Hartley, Colpitts, RC-oscillators and crystal oscillator (RR1)

SECTION-B

Band-pass amplifiers: Parallel resonant circuit and its bandwidth. Tuned primary and tuned secondary amplifiers (RR1)

Power amplifiers: Operating conditions, Power relations, Nonlinear distortion, Class A power amplifier, Push-pull principle, Class B Push pull amplifier (RR1)

Fundamentals of modulation: Frequency spectrum in amplitude modulation, Methods of amplitude modulation, Frequency modulation, Linear demodulation of AM signals, SSB system, AM and FM transmission, Receiving systems (RR1)

Operational amplifiers: Ideal operational amplifier. Inverting and non-inverting amplifiers. Differential amplifiers. CMMR. Internal circuit of operational amplifier. Examples of practical operational amplifier. Operational amplifier characteristics. DC and AC characteristics, slew rate (RR2)

Text Books:1. Electronics Fundamentals and Applications: John D. Ryder (5th Ed.), PHI, New Delhi2. Linear Integrated circuits: D.Roy Choudary and Shail B.Jain, New age international

Publishers

AP 1.1.4 Elective Paper: Option (ii) REMOTE SENSING


Out of 80 Marks, internal assessment (based on two mid-semester tests/ internal examination, written assignment/project work etc. and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

Instruction for the Paper Setter: The question paper will consist of three sections A, B and C. Each of sections A and B will have four questions from respective sections of the syllabus. Section C will have 10 short answer type questions, which will cover the entire syllabus uniformly. Each question of sections A and B carry 10 marks. Section C will carry 20 marks.

Instruction for the candidates: The candidates are required to attempt two questions each from sections A and B, and the entire section C. Each question of sections A and B carries 10 marks and section C carries 20 marks. Use of scientific calculators is allowed.

SECTION A

History and scope of remote sensing: Milestones in the history of remote sensing, overview of the remote sensing process, A specific example, Key concepts of remote sensing, career preparation and professional development.

Introduction: Definition of remote sensing, Electromagnetic radiation, Electromagnetic Spectrum, interaction with atmosphere, Radiation-Target, Passive vs. Active Sensing, Characteristic of Images.

Sensors: On the Ground, In the Air& in Space, Satellite characteristics, Pixel Size and Scale, Spectral Resolution, Radiometric Resolution, Temporal Resolution, Cameras and Aerial photography, Multispectral Scanning, thermal Imaging, Geometric Distortion, Weather Satellites, Land Observation Satellites, Marine Observation Satellites, Other Sensors, Data Reception.

SECTION B

Microwaves: Introduction, Radar Basics, Viewing Geometry & Spatial Resolution, Image Distortion, Target Interaction, Image Properties, Advanced Applications, Polarimetry, Airborne vs. Spaceborne, Airborne & Spaceborne Systems.

Image Analysis: Visual Interpretation, Digital processing, Preprocessing, Enhancement, Transformations, Classification, Integration.

Applications: Agriculture—Crop Type Mapping and Crop Monitoring; Forestry---Clear cut Mapping, Species identification and Burn Mapping; Geology---Structural Mapping & Geological Units; Hydrology-----Food Delineation & Soil Moisture; Sea Ice----Type & Concentration, Ice Motion; Land Cover----Rural/Urban Change, Biomass Mapping; Mapping-----Planimetry, DEMs, Topo Mapping; Oceans & Coastal-----Ocean features, Ocean Colour, Oil Spill Detection.

Text Books:1. Introduction to Remote Sensing : James B. Cambell2. Fundamentals of Remote Sensing: Natural Resources, Canada Centre of Remote Sensing.

AP 1.1.4 Elective Paper: Option (iii) MICROWAVE AND ITS PROPAGATION





Use of scientific calculators is allowed.

SECTION A

Microwave linear beam tubes: Conventional vacuum tubes, Klystrons, resonant cavities, velocity modulation process, branching process, output power and beam loading; multi cavity klystron amplifiers, reflex klystrons, helix travelling wave tubes, slow wave structures.

Microwave crossed field tubes: Magnetron oscillators: cylindrical, linear and coaxial, forward wave crossed field amplifier, backward wave crossed field amplifier, backward wave crossed field oscillator, their principle of operation and characteristics.

Microwave transistor and tunnel diodes: Microwave bipolar transistors, physical structures, configurations, principles of operation, amplification phenomena, power-frequency limitations, heterojunction bipolar transistors, physical structures, operational mechanism and electronic applications, microwave tunnel diodes, principles of operation, microwave characteristics.

Microwave field effect transistors: Junction field effect transistors, metal semiconductor field effect transistors, high electron mobility transistors, metal oxide semiconductor field effect transistors, physical structures, principle of operation and their characteristics. MOS transistor and memory devices: NMOS, CMOS and memories. Charged coupled devices: Operational mechanism, surface channel CCD's dynamic characteristics.

SECTION B

Transferred electron devices: Gunn effect diodes, Ridley-Walkins-Hilsum theory, modes of operation, LSA diodes, InP diodes, CdTe diodes, microwave generation and amplification.

Avalanche transit time devices: Read diode, IMPATT diodes, TRAPATT diodes, BARITT diodes, their physical structure, principle of operation and characteristics.

Microwave measurements: Measurement of impedance, attenuation, insertion loss, coupling and directivity, frequency, power and wavelength at microwave frequencies.

Microwave transmission lines: Transmission line equations and solutions, reflection coefficient and transmission coefficient, standing wave and standing wave ratio, line impedance and admittance, Smith chart, impedance matching. Microwave cavities, microwave hybrid circuits, directional couplers, circulators and isolators.

Text Books:1. Microwave Devices and Circuits: Sameul Y. Liao, Pearson Education2. Microwaves: K.C. Gupta, Wiley Eastern Limited.

AP 1.1.5 Laboratory Practice: i) Electronic Lab ii) Laser-Optics Lab

Maximum Marks: 80 Time allowed: 3 HoursPass Marks: 45% Total teaching hours: 100

Out of 80 Marks, internal assessment (based on seminar, viva-voce of experimental reports, number of experiments performed and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

This laboratory comprises of experiments based on Lasers and Optics in one group and Electronics in the other group. Each student will be placed in one of the two groups during the entire semester.

GROUP- I ELECTRONICS EXPERIMENTS : (10 out of the followings)

1. Study the gain frequency response of a given RC coupled BJT, CE amplifier.

2. Study of Clipping & Clamping circuits.

3. Study of shunt capacitor filter, inductor filter, LC filter and filter using Bridge Rectifier.

4. Find the energy gap of a given semi conductor by reverse bias junction method.

5. To calculate the temperature coefficient of Thermistor.

6. Verify De-Morgan’s law and various combinations of gates using Logic gates circuit.

7. Study of various types of Flip-Flops.

8. To study various Oscillators (Hartley, Colpit, RC Phase shift etc.).

9. To study Amplitude Modulation and De-Modulation and calculate modulation index.

10. To study characteristics of FET and determine its various parameters.

11. Study the characteristics of Tunnel Diode.

12. To study 2 bit, 3 bit and 4 bit Adder & Subtractor.

13. Study the characteristics of basic Thyristors (SCR, MOSFET, UJT, TRIAC etc.).

14. Use of Transistor as a push pull amplifier (Class ‘A’, ‘B’ and ‘AB’).

15. Application of transistor as a series voltage regulator.

16. Study of biasing techniques of BJT.

17. To study Frequency Modulation and Demodulation.

18. Study of transistor as CE, CB and CC amplifier.

19. Fourier series analysis of square, triangular and rectified wave signals.

GROUP- II LASERS AND OPTICS EXPERIMENTS: (10 out of the followings)

1. To study the optical bench model of microscope and to determine the numerical aperture of the microscope.

2. To study the optical bench model of telescope and to determine the angular field of view and magnifying power by entrance and exit pupil method.

3. To study the characteristics of solar cell.

4. To study the magnetostriction in an iron rod using Michelson interferometer.

5. To study the optical thickness of mica sheet using channel spectrum interferometry.

6. To determine the Planck’s constant using photovoltaic cell.

7. To obtain the coherence matrix and stokes parameters for (i) unpolarized light (ii) polarized light and hence to determine their degree of polarization.

8. To study the aberrations of a convex lens.

9. To study the electro-optic effect in LiNbO3 crystal using He-Ne laser.

10. To study B-H curve.

11. To study the characteristics of optoelectronic devices (LED, Photodiode, Photodiode, Phototransistor, LDR).

12. To study the diffraction pattern by pin hole, single slit, double slit and grating and to calculate the wavelength of He-Ne laser.

13. To study microwave optics system for reflection, refraction, polarization phenomena.

14. To calibrate the prism spectrometer using mercury lamp and to determine the refractive index of material of the prism for a given wavelength of light.

15. Measurement of Brewster angle and refractive index of materials like glass and fused silica (with He-Ne laser) with a specially designed spectrometer.

16. Particle size determination by diode laser

17. Study of optical fiber communication kit.

AP 1.1.6 Computer Laboratory


Out of 40 Marks, internal assessment (based on performance of the candidate in the computer lab and attendance) carries 10 marks, and the final examination at the end of the semester carries 30 marks.

This laboratory comprises of (any ten of the following) physics problems to be solved using computer.

1. To print even and odd numbers between given limit

2. To generate prime numbers between given limit.

3. To construct Fibonacci series.

4. To find maximum and minimum number among a given data.

5. To find area of a triangle.

6. To find factorial of a number.

7. To find roots of a quadratic equation.

8. To construct AP and GP series.

9. To construct Sine and Cosine series.

10. Conversion of temperature scale.

11. Addition of two matrices.

12. Motion of horizontally thrown projectile.

13. Finding mean and standard deviation of a given data.

14. To find perfect numbers.

AP 1.1.7 Workshop (Mechanical/ Optical)


Out of 60 Marks, internal assessment (based on performance in the workshop and attendance) carries 15 marks, and the final examination at the end of the semester carries 45 marks.

In the workshop students will fabricate mechanical jobs (spanner, U-fitting, screw driver, wooden- cross etc.) in one group and optical jobs (Lens, prism, mirror etc.) in the second group. Each student will be placed in one the two groups during the entire semester.

Semester –II

AP 1.2.1 DIGITAL ELECTRONICS






SECTION A

Binary, octal and hexadecimal number systems, Inter-conversion of binary to decimal, Decimal to binary, Octal to binary, hexadecimal to binary numbers, Binary arithmetic.

Binary codes, the 8421 code, Gray code and ASCII codes.

Boolean algebra and logic gates-Boolean variables, NOT, AND, OR, NAND, NOR and exclusive OR operation, Boolean identities and laws of Boolean algebra, DeMorgan's theorem, Combinational and sequential logic systems, Minterm and Maxterm and mapping.

Switching properties of semiconductor devices, Diode, BJT and FET as DC and AC switches, Combinational logic circuits using digital ICs.

Sequential and combinational systems. RS, JK, D and T flip-flops, Counters, Synchronous counters, Serial, parallel and mixed counters

SECTION B

Shift registers and ring counters, Universal shift registers

Semiconductors memories, Memory organization and operation, Expanding memory size, Classification and characteristics of memories, Sequential memory, Read only memory, Read and write memory.

Variable register network, Binary ladder, D/A convertor, D/A accuracy and resolution, A/D converters, Simultaneous conversion, Counter method, A/D converters

Characteristics of digital ICs, Classification of logic families, Digital IC packages.

Text Books:1. Digital Principles: A.P. Malvino and D.P. Leach, Tata McGraw-Hill Pub. Co. Ltd. New Delhi.2. Modern Digital Electronics: R.P. Jain, Tata McGraw-Hill Pub. Co. Ltd., New Delhi.

Reference Books:1. Microelectronics: Jacob Millman & Arvin Grabel (3rd Ed.), McGraw Hill Book Co., New Delhi.2. Digital Systems: Principle and Applications: Ronald J. Tocci (Vth Ed.), PHI, New Delhi.3. An Introduction to Digital electronics: M.Singh, Kalyani Publishers, New Delhi.

AP 1.2.2 RADIATION PHYSICS






SECTION A

Interaction of Radiation with Matter:Interaction of electromagnetic radiations: Different photon interaction processes viz. photoelectric effect, Compton scattering and pair production. Minor interaction processes, Energy and Z dependence of partial photon interaction processes. Attenuation coefficients, Broad and narrow beam geometries. Multiple scattering.

Interaction of charged particles: Elastic and inelastic collisions with electrons and atomic nucleus. Energy loss of heavy charged particles. Range-energy relationships, Straggling. Radiative collisions of electrons with atomic nucleus.

Nuclear Detectors and Spectroscopy: General characteristics of detectors, Gas filled detectors, Organic and inorganic scintillation detectors, Semi conductor detectors [Si(Li), Ge(Li) HPGe]. Room temperature detectors, Gamma ray spectrometers. Gamma ray spectrometry with NaI(Tl) scintillation and semiconductor detectors.

SECTION B

Nuclear spectrometry and applications: Analysis of nuclear spectrometric data, Measurements of nuclear energy levels, spins, parities, moments, internal conversion coefficients, Angular correlation, Perturbed angular correlation, Measurement of g-factors and hyperfine fields.

Analytical Techniques: Principle, instrumentation and spectrum analysis of XRF, PIXE and neutron activation analysis (NAA) techniques. Theory, instrumentation and applications of electron spin resonance spectroscopy (ESR). Experimental techniques and applications of Mossbauer effect. Rutherford backscattering. Applications of elemental analysis, Diagnostic nuclear medicine, Therapeutic nuclear medicine.

Text Books:1. The Atomic Nucleus: R. D. Evans, Tata Mc Graw Hill, New Delhi2. Nuclear Radiation Detectors: S. S. Kapoor and V. S. Ramamurthy, New Age, International,

New Delhi.3. Radiation Detection and Measurements: G. F. Knoll, Wiley & Sons, New Delhi4. Introductory Nuclear Physics: K. S. Krane, Wiley & Sons, New Delhi5. An Introduction to X-ray Spectrometry: Ron Jenkin, Wiley6. Techniques for Nuclear and Particle Physics Experiments: W. R. Leo, Narosa Publishing

House, New Delhi.7. Introduction to experimental Nuclear Physics: R. M. Singru, Wiley & Sons, New Delhi.

AP 1.2.3 QUANTUM MECHANICS






SECTION AWave Mechanics: Review of wave mechanical principles. Time independent Schrodinger equation in one, two and three dimensions. Eigen values and Eigen functions. Bound states. Discrete eigen values. Orthogonality of eigen functions. Completeness of eigen functions. Box and function normalization. Expectation values of observables. Uncertainty principle.

Particle in a one dimensional box with finite walls. Two dimensional square with infinite walls. Three dimensional rectangular box with infinite walls and three dimensional square well potential. Isotropic Harmonic oscillator. Degeneracy.

Matrix Mechanics: Postulates of quantum mechanics. Hilbert space. Matrix representation of wave functions and operators. Dirac bra and Ket notations. Change of basis. Harmonic oscillator problem in matrix mechanics creation, destruction and number operators. Orbital angular momentum operators in their polar form . Commutation relations. and Matrix representation of orbital angular momentum operators. Eigen vectors values eigen of L2, Lz spin angular momenta and Pauli spin matrices.

Addition of angular momenta. Clebsch-Gordan coefficients. C.G. coefficients of .

SECTION BApproximation methods for bound states: Stationary non degenerate perturbation theory, Ist and second order correction to energy levels, Ist order correction to wave functions, Anharmonic oscillator

Degenerate perturbation theory. Normal Zeeman effect and stark effect of the first excited state of hydrogen.

The Rayleigh Ritz variational method for ground and excited states. Ground state of He atom perturbation and vibrational approaches and their comparison.

Van der Waal's interaction. Perturbation and varational calculations.

One dimensional WKB approximation. Asymptotic behaviour of solutions. Linear turning points. Connection formula and their application to bound state and barrier penetration.

Collision Thoery: Two particle scattering problem. Differential and total scattering cross-section. Lab and CM system of coordinates. Scattering of a particle by a central field. Partial wave analysis. Phase shifts S & P wave scattering. Ramsauer Townsend effect. Resonant scattering. Scattering for a three dimensional square well and rigid sphere. Integral equation for scattering problem. Born approximation. Validity of Born approximation. Screened Coulomb potential.

Text Books:1. Quantum Mechanics: L.I. Schiff (Int. Student Ed.),Tata Mc Graw Hill, New Delhi.2. Quantum Mechanics: J.L. Powell and B. Craseman (Narosa Publishing House, New Delhi.3. Quantum Mechanics; Mathews & Venkatesan, Tata Mc Graw Hill, New Delhi.

AP 1.2.4 Elective Paper: Option (i) APPLIED OPTICS






SECTION A

Fourier Optics: Maxwell's equations and the statement of the diffraction problem in terms of the transmission function. Simple Huygen-Fresnel theory to explain diffraction. Different regions of the diffraction. Fresnel and Fraunhofer approximations. Concept of spatial frequency. Importance of Fourier transformation in optics and its physical interpretation. Physical interpretation of convolution and delta function transform theorems. (RR1)

Use of the Fourier transform to explain Fraunhofer diffraction at a circular aperture. Fraunhofer diffraction at rectangular aperture under various situations. Fresnel diffraction at rectangular aperture and straight edge. Fresnel diffraction and lens. Limitation of geometrical optics. Free space propagation of waves. Phase transmission functions and lens. (RR1)

SECTION BPolarization: Polarization and double refraction. Explanation of double refraction. Polarization devices: Nicol, Glan, Glan-Thompson, Wollaston, Rochon and Severmont prisms. Wave propagation in anisotropic media. Spatial frequency filtering: The Fourier transforming property of a thin lens. Applications of spatial frequency filtering: Low pass, High pass, Band pass filters. Phase contrast microscope. Image debluring (RR1 & RR2)

Holography: Basic principles, Coherence requirements. Resolution. Gabor holography and distinction with off-axis holography. Fourier transform holograms. Lensless Fourier transform holograms. Computer generated holograms. Volume holograms.

Applications of holography: Microscopy, Interferometry, Character recognition. Holography in optical signal processing. Vander Lugt filter based on Mach-Zender and Rayleigh interferometers. Matched filtering and Fourier transform hologram (RR2)

Text Books:1. Lasers and Optical Engineering: P. Das, Narosa Publishing House, 19922. Optical Electronics: A.K. Ghatak and K. Thyagrajan, Cambridge Univ. Press, 1989

AP 1.2.4 Elective Paper: Option (ii) MATHEMATICAL PHYSICS AND CLASSICAL MECHANICS






SECTION A

Cartesian Tensors: Coordinate transformations. Three dimensional rotations. Transformation of vector components under three dimensional rotations. Direct product of two vectors. Tensors of higher rank. Symmetric and antisymmetric tensors. Kronecker and alternating tensors and their isotropy property. Contraction of tensors and differentiation of tensor fields. Expressions for gradient divergence and curl in tensor notation. Vector formulae in tensor notation.

Linear Vector Spaces: Definition, linear independence of vectors, basis and dimensionality. Scalar products of vectors. Orthonormal basis. Gram Schmidt orthogonalization process. Matrix representation of vectors and linear operators. Infinite dimensional vector spaces. Hilbert spaces.

Complex Variables: Complex numbers and variables. Polar form of complex numbers. Functions of complex variables. Cauchy Riemann differential equations. Singularities and their classification. Cauchry integral theorem and formulae. Taylor and Laurent's series, The Cauchy residue theorem and its application to evaluation of real integrals.

SECTION BRigid body dynamics: Angular momentum and kinetic energy of rotating rigid body about a fixed point, inertia tensor, Eigen values of inertia tensor, Principal moments and principal axes transformation.

Special Theory of relativity: Lorentz transformation in vector form and orthogonality of Lorentz transformation, Lorentz orthogonal transformation matrix, Equivalent rotation angle and Einstein addition law for parallel velocities, Intervals in four-space and Invariance of Space-time interval, covariant formulation of four space and representation of various vectors in four-space, covariant formulation of Force, momentum and energy equation in Minkowski space, Lagrangian formulation of relativistic mechanics.Relativsitic motion of a particle under a constant force. Relativistic one dimensional harmonic oscillator. Continuous systems and fields: Transition from discrete to continuous systems. Lagrangian and Hamiltonian formalisms, Stress-energy tensor and conservation laws. Scalar and Dirac fields (only definitions).

Text Books:1. Cartesian Tensors: Harold Jefferies, Combridge University, Press2. Linear Vector Spaces: John Dettman (Hilderbrand)3. Complex Variables: Murrey R. Speigel, Schaum Series, Mc Graw Hill Publication4. Classical Mechanics: H. Goldstein, Narosa Publishing House, New Delhi.

AP 1.2.4 Option (iii) COMPUTER FUNDAMENTALS AND PROGRAMMING WITH C++






SECTION AComputer organization: Hardware, Memory, Control unit, Arithmetic and logic unit, Input and output devices, software, Programing languages with special reference to C and C++, Assembler, Interpreter and compiler, Application software.

Problem solving with a computer: Problem analysis, Algorithm development, The quality of algorithm, Flowcharts, Program coding, Compilation and execution.

Data types and statements: Identifiers and keywords, Constants, String constants, Numeric constants, Character constants, C++ operators, Arithmetic operators, Assignment operators, Comparison and logic operators, Bitwise logic operators, Special operators, Type conversion.

Writing a programme in C++: Declaration of variables, Statements, Simple C++ programs, Features and iostream.h, Keyword and screen I/O, Manipulation functions, Predefined manipulators, Input and output (I/O) stream flags.

SECTION BControl statements: Conditional expressions, If- statement, If else statement, Switch statement, Loop statements, for- loop, While- loop, do while- loop, Breaking control statements, Break statement, Continue statement and goto statement.

Functions and program structures: Defining a function, Return statement, Types of functions, Actual and formal arguments, Local and global variables, Default arguments, Multifunction program, Storage class specifiers, Automatic variables, Register variables, Static variables, External variables.

Arrays: Array notation, Array declaration and array initialization, Processing with array, Arrays and functions, Multidimensional arrays, Character array.

Pointers: Pointer declaration, Pointer operator, Address operator, Pointer expressions, Pointer arithmetic, Pointer and functions, Call by value, Call by reference.

Structures, unions and bit fields: Declaration of structures, Initialization of structures, Functions of structures, Unions, The union tag, Processing with union, Initialization of unions, Idea of bit fields.

Text Books:1. Programming with C++: D. Ravichandran (2nd Ed.), Tata Mc Graw-Hill Pub. Co. Ltd.2. Object-oriented Programming with C++: R. Balaguruswamy, Tata Mc Graw-Hill Pub. Co.

Ltd.

AP 1.2.5 Laboratory Practice: i) Electronic Lab ii) Laser-Optics Lab


Out of 80 Marks, internal assessment (based on seminar, viva-voce of experimental reports, number of experiments performed and attendance) carries 20 marks, and the final examination at the end of the semester carries 60 marks.

This laboratory comprises of experiments based on Lasers and Optics in one group and Electronics in the other group. Each student will be placed in the group (different from that in the first semester) during the entire semester.

GROUP- I ELECTRONICS EXPERIMENTS : (10 out of the followings)

1. Study the gain frequency response of a given RC coupled BJT, CE amplifier.

2. Study of Clipping & Clamping circuits.

3. Study of shunt capacitor filter, inductor filter, LC filter and filter using Bridge Rectifier.

4. Find the energy gap of a given semi conductor by reverse bias junction method.

5. To calculate the temperature coefficient of Thermistor.

6. Verify De-Morgan’s law and various combinations of gates using Logic gates circuit.

7. Study of various types of Flip-Flops.

8. To study various Oscillators (Hartley, Colpit, RC Phase shift etc.).

9. To study Amplitude Modulation and De-Modulation and calculate modulation index.

10. To study characteristics of FET and determine its various parameters.

11. Study the characteristics of Tunnel Diode.

12. To study 2 bit, 3 bit and 4 bit Adder & Subtractor.

13. Study the characteristics of basic Thyristors (SCR, MOSFET, UJT, TRIAC etc.).

14. Use of Transistor as a push pull amplifier (Class ‘A’, ‘B’ and ‘AB’).

15. Application of transistor as a series voltage regulator.

16. Study of biasing techniques of BJT.

17. To study Frequency Modulation and Demodulation.

18. Study of transistor as CE, CB and CC amplifier.

19. Fourier series analysis of square, triangular and rectified wave signals.

GROUP- II LASERS AND OPTICS EXPERIMENTS: (10 out of the followings)

1. To study the optical bench model of microscope and to determine the numerical aperture of the microscope.

2. To study the optical bench model of telescope and to determine the angular field of view and magnifying power by entrance and exit pupil method.

3. To study the characteristics of solar cell.

4. To study the magnetostriction in an iron rod using Michelson interferometer.

5. To study the optical thickness of mica sheet using channel spectrum interferometry.

6. To determine the Planck’s constant using photovoltaic cell.

7. To obtain the coherence matrix and stokes parameters for (i) unpolarized light (ii) polarized light and hence to determine their degree of polarization.

8. To study the aberrations of a convex lens.

9. To study the electro-optic effect in LiNbO3 crystal using He-Ne laser.

10. To study B-H curve.

11. To study the characteristics of optoelectronic devices (LED, Photodiode, Photodiode, Phototransistor, LDR).

12. To study the diffraction pattern by pin hole, single slit, double slit and grating and to calculate the wavelength of He-Ne laser.

13. To study microwave optics system for reflection, refraction, polarization phenomena.

14. To calibrate the prism spectrometer using mercury lamp and to determine the refractive index of material of the prism for a given wavelength of light.

15. Measurement of Brewster angle and refractive index of materials like glass and fused silica (with He-Ne laser) with a specially designed spectrometer.

16. Particle size determination by diode laser

17. Study of optical fiber communication kit.

AP 1.2.6 Computer Laboratory


Out of 40 Marks, internal assessment (based on performance of the candidate in the computer lab and attendance) carries 10 marks, and the final examination at the end of the semester carries 30 marks.

This laboratory comprises of any ten of the following physics problems to be solved using

computer.

1. To generate Frequency Distribution Table.

2. Solution of a differential equation by RK2 method.

3. To find area under a curve by Trapezoidal Rule and Simpson’s Rule

4. Gauss elimination method.

5. Multiplication of Two Matrices.

6. Motion of Projectile thrown at an Angle.

7. Numerical Solution of Equation of Motion.

8. Simulation of planetary motion.

9. Root of an equation by Newton- Raphson method.

10. Sorting numbers by selection sort.

11. Solution of a differential equation by RK4 method.

12. Fitting straight line through given data points.

13. Roots of an equation by secant method.

14. Newton interpolation.

AP 1.2.7 Workshop (Mechanical/ Optical)


Out of 60 Marks, internal assessment (based on performance in the workshop and attendance) carries 15 marks and the final examination at the end of the semester carries 45 marks.

In the workshop students will fabricate mechanical jobs (spanner, U-fitting, screw driver, wooden cross etc.) in one group and optical jobs (Lens, prism, mirror etc.) in the second group. Each student will be placed in the group (different from that in the first semester) during the entire semester.

For Other Departments Students: Qualifying Paper

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