Suresh Gyan Vihar University Courses

M.Sc. (Physics)

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Duration: 2 Years

Eligibility: Graduation

Course Structure

Course Code	Course Title
Semester - I
PY-501	Classical Mechanics
PY-503	Mathematical Phys.
PY-505	Electronics
PY-507	Quantum Mechanics-I
PY-551	Laboratory -1
PY-553	Laboratory-II
Semester - II
PY-502	Statistical Mechanics
PY-504	Nuclear Physics
PY-506	Electrodynamics
PY-508	Quantum Mechanics-II
PY-552	Laboratory-III
Semester - III
PY-601	Atomic,     Molecular     and Laser Physics
PY-603	Solid State Physics
PY-605	Numerical  methods and Computer Programming
PY-515, PY-517, PY-519	Elective –A
PY-553	Laboratory-IV
Semester - IV
PY-602	Instr. Methods and Adv. Analytical Techniques
PY-604	Physics of Semiconductors
PY-514, PY-516, PY-518	Elective – B
PY-520, PY-522, PY-524	Elective – C
PY-554	Project
List of Electives
Elective - A
PY515	Solar Physics
PY517	Plasma Physics
PY519	Microwave Electronics
Elective - B
PY-514	Lasers and Opto-Electronics
PY-516	Atmospheric Physics
PY-518	Nano-structured Materials and Applications
Elective - C
PY520	Condensed Matter
PY522	Electronics & Communication
PY524	Introduction to Astronomy & Astrophysics

 

Course Detail

Classical Mechanics  PY-501

Holonomic and non-holonomic constraints, Newton’s equation with constraints, virtual work, generalized coordinates, D’ Alembert’s principle Lagrange’s equation and its applications, calculus of variations, variation principles and Lagrange’s equation. Cyclic coordinates, Hamilton’s equations, method of Lagrange’s multipliers, conservation principle and Noether’s theorem, Canonical transformation, Legendre transformations, Poisson brackets, Liouville theorem, Hamilton - Jacobii equation. Central force, Kepler’s problem, Scattering of particles in a central force field, Rutherford formula, Eulerian angles, Euler theorem, Force free motion of a rigid body, Coriolis force, small oscillations and normal modes.

 

Statistical Mechanics PY-502

Review of thermodynamics: Introduction to statistical methods: description of system of particles, statistical distribution, phase space, statistical ensembles Basic principles of canonical, micro canonical and grand canonical ensembles, method of calculation using ensemble approach and its applications to classical systems, partition functions and properties, calculation of thermodynamic quantities, density and energy fluctuations. Maxwell – Boltzmann statistics, Quantum distribution functions, B-E and F-D statistics, Boltzmann Transfer Equation and its application to transport phenomena, B-E condensation, laser cooling of atoms, thermo-dynamics of phase transitions, Landau’s theory, elementary concepts of non-equilibrium, statistical mechanics.

 

Mathematical Physics  PY-503

Matrices, vector spaces, eigenvalues and eigenvectors, complex variables, conformal mapping and its applications, Cartesian tensors with applications in Physics. Review of wave, heat and Laplace partial differential equations, Laplace transforms and their properties, Laplace transform of periodic functions, Application of Laplace transform in solving linear, differential equations, , Fourier transforms and its applications. Special functions: Bessel functions, Spherical Bessel functions, Legendre’s, Hermite and Laguerre polynomials, Green’s function and its applications, Group theory and its applications.

 

Nuclear Physics PY-504  

Nuclear binding energy, electric and magnetic moments, nuclear force: deuteron, n-p and p-p scattering, semi-empirical mass formula: liquid drop model, nuclear shell model, shell model predictions, selection rules, nuclear isomerism, collective nuclear model. Nuclear decay, theories for , β and γ – decay, transition probabilities, selection rules, general characteristics of weak interaction. Nuclear reactions, partial wave analysis, compound nucleus formation, resonance scattering and reaction, optical model. Reactor physics: fission reactors, schemes for nuclear fusion. Particle accelerators: pelletron, synchrotron and colliders, nuclear detectors: solid state detectors. Introduction to particle physics: symmetries of elementary particles, quark model.

 

Electronics PY-505

Differential amplifier circuit, operational amplifier: characteristics and applications, oscillators and wave shaping circuits: multi-vibrators and trigger circuits, voltage and switching regulators, comparator. Digital electronics: flip-flops, counters, signal averaging, D/A and A/D converter.  Microwave engineering: klystron and wave guides. Introduction to Microprocessors.

 

Electrodynamics PY-506

Review of electrostatics and magnetostatics. Polarization and conductivity. Boundary value problems using Poisson’s and Laplace’s equations. Maxwell’s equations for time varying fields. Plane waves in dielectrics and conductors. Wave propagation in plasmas. Surface waves and medium frequency communication, wave guides, transmission lines. Linard-Wiechert potentials of a point charge. Total power radiated by an accelerated charge. Dipole antenna, antenna array, covariant form of electrodynamics equations.

 

Quantum Mechanics – I PY-507

State vector, vector spaces, Hilbert space, Dirac notation, operators, Schrodinger equation, wave function, wave packet, stationary states, eigen values and eigen functions. Born’s interpretation, expectation values and Ehrenfest’s theorem, uncertainty principle, one dimensional potential problems. Harmonic oscillator, two body problem, hydrogen atom. Symmetries, conservation laws, invariance under space and time translations and space rotation, angular momentum, spin, addition of angular momenta, tensor operators.

 

Quantum Mechanics – II PY-508

Time independent perturbation theory, normal Zeeman and Stark effects, WKB approximation and variational methods. Time dependent perturbation theory, Fermi Golden rule. Interaction of radiation with matter, radiation field quantization, Spontaneous emission, absorption, induced emission, dipole transitions, selection rules, identical particles. Non-relativistic scattering, solution of scattering problem by the method of partial wave analysis, optical theorem, Born approximation and its validity for scattering problems, Relativistic formulation and Dirac equation: plane wave solution of free particles.

 

Elective-B

Lasers and Opto-Electronics PY-514

Laser criterion, types of lasers: masers, molecular lasers, nitrogen lasers, tunable dye lasers, semiconductor lasers. Applications of lasers: holography, materials processing, medical appli cations; optical communication: fibre optical communication systems and integrated optics. Dispersions and losses in optical fibre, modulation of light: birefringence, electro-optic effect, modulators, magnato-optic devices, Acousto-optic effect, Non-linear optics, semiconductor optical amplifiers, display devices: luminescence, photoluminescence, cathodoluminescence, plasma displays, photo detectors, solar cells, light emitting diode.

 

Elective-A

Solar Physics PY-515

Solar Energy: origin, solar constant, spectral distribution of solar radiation, absorption of solar radiation in the atmosphere, global and diffused radiation, seasonal and daily variation of solar radiation, measurement of solar radiation. Photo thermal conversion and storage of solar energy: concentrating/non-concentrating solar  collectors, efficiency and its dependence on various parameters, selective coatings – materials and properties, distillation, drying, cooking, air heating, refrigeration and thermal power generation. Solar space conditioning – energy requirements in buildings, passive system architecture, performance and design, green house effect and storage and thermal energy. Photovoltaic conversion of solar energy: PV effect, materials, fabrication technologies for solar cells, different types of solar cells, efficiency limiting factors, power, spectral response, fill factor, temperature effect. Photovoltaic systems: sizing, designing, performance and applications.

 

Nanostructured Materials And Applications PY-516

Background to nanostructures, synthesis and properties of nanostructures: zero dimensional nanostructures - nanoparticles; one-dimensional nanostructures - nanowires and nanorods; twodimensional nanostructures - thin films, self assembly of atoms; special nanostructures – quantum nanostructures; carbon fullerenes and nanotubes; nanocomposites. Chracterisation of nano-structures: XRD, SEM, TEM, STM and AFM, optical techniques, magnetic resonance. Applications of nanotechnology to: environment and energy, optics, photonics and solar energy, nanoeletronics.

 

Plasma Physics PY-517

Basic properties and occurrence of plasma, criteria for plasma behaviour, Plasma oscillations, quasineutrality and Debye shielding, the plasma parameters, Saha equation, brief discussion of methods of laboratory plasma production. Elementary ideas about plasma diagnostics, electrostatic and magnetic probes. Charged particle motion and drifts: guiding centre motion of charged particles, motion in uniform electric and magnetic fields, motion in non-uniform magnetic field, principle of magnetic mirror, motion in non-uniform electric field for small larmour radius, time varying electric field and polarization drift, time varying magnetic field, adiabatic invariance of magnetic moment, plasma fluid equations. Collision and diffusion parameters: collision in fully ionized plasma, plasma resistivity, diffusion in fully ionized plasmas, solution of diffusion equation, equilibrium and stability: hydromagnetic equilibrium, concept of magnetic pressure, equilibrium of a cylindrical pinch, diffusion of magnetic field into a plasma, classification of instabilities, plasma processing of materials, plasma diode, MHD Power generation, electromagnetic wave propagation in ionosphere and other media, Laser driven fusion and other applications.

 

Microwave Electronics PY-519

Introduction to microwaves and its frequencys spectrum, Application of microwaves. Wave Guides :

(a) Rectangular wave guides : Wave equation & its solutions, TE & TM modes. Dominant mode and choice of wave guide Dimensions Methods of excitation of wave guide.

(b) Circular wave guide-wave equation & it solutions, TE, TM & TEM modes.

(c) Attenuation - Cause of attenuation in wave guides, wall current. & derivation of attenuation constant, Q of the wave guide.

1. (a) Resonantors : Resonant Modes of rectangular and cylindrical cavity resonantors, Q of the cavity resonantors, Excitation techniques, Introduction to Mircostrip and Dielectric resonantors, Frequency meter.

(b) Farrites : Microwave propagation in ferrites, Farady rotatiion, Devices employing Faraday rotation (isolator, Gyrator, Circulator). Introduction to single crystal ferromagnetic resonators, YIG tuned solid state resonators.

2. Microwave tubes : Space charge spreading of an electron beam, Beam focussings. Klystrons : Velocity Modulation, Two Cabvity Klystron, Reflex Klystron Efficiency of Klystrons. Magnetrons : Types &  description, ehoeretical relations between Electric & Magnetic field of oscillations. Modes of oscillation & operating characteristics. Travelign wave tubes : O & M type traveling wave tubes. Gyrotorons : Constructions of different Gyrotrons, Field - Particle Interaction in Gyrotron.

3. Microwave Measurement :

(a) Microwave Detectors : Power, Frequency, Attenuation, Impedance Using smith chart, VSWR, Reflectometer, Directivity, Coupling using direction coupler.

(b) Complex permitivity of material & its measurement: definition of complex of solids, liquids and powders using shift of minima method.

 

Elective -C

Condensed Metter Physics  PY-520

Structure Factor : Static structure factor and its relation with the pair correlation function. Determinationof structure factor by X-ray and neutron scattering. Inelastic neutron scattering and dynamic structure factor, space time correlation function and its relation with dynamic structure factor, properties of space time correlation function. Langevin's equation for Browninan Motion and its modifications. Velocity autocorelatiion function, mean square displacement, Relation between velocity autocorelation function and diffusion coefficient.

Liquid Metals : Metallic interactions-Kinetic energy, electrostatic exchange and correlation, Pseudopotential formalism, diffraction model, structure factor, form factor for local and nonlocal potentials, energy eigen states, dielectric screening. Energy wave number characteristics, calculation of phonone dispersion of liquid metals. Band structure energy in momentum and direct space. Ziman's resistivity formula, Green function method for energy bands in liquid metals.

Quantum Liquids : Distinction between classical and quantum liquids, critetria for freezing, phase diagram of He4, He I and He II Tisaza's two fluid model, entropy filter, Fountain effect, superfluid film vehicle, Viscosity and specific heat of He4, first sound, second sound, third sound and fourth sound, Landau theory: Rotons and  Phonis, t-matrix theory of superfluid He. Basic differences in superfluidity in He3 and He4.

Exotic Solids : Structure and symmetries of liquids, liquid crystals and amorphous solids. Aperiodic solids and quasicrystals; Fibonanccy sequency, Penrose lattices and their extension to 3-dimensions, Special carbon solids. Fullerences and tubules; formation and characterization of fullerences and tubules. Single wall and multivwall carbon tubules. Electronic properties of tubules. Carbon nanotubule based electronic based devices Definition and properties of nanostrctured materials. Methodsof synthesis of nanostructured materials. Special experimental techniques for characterization of nanostrcutred materials. Quantum size effect and its applications.

 

Electronics & Communication  PY-522

Introduction to microwaves and its frequencys spectrum, Application of microwaves. Wave Guides :

(a) Rectangular wave guides : Wave equation & its solutions, TE & TM modes. Dominant mode and choice of wave guide Dimensions Methods of excitation of wave guide.

(b) Circular wave guide-wave equation & it solutions, TE, TM & TEM modes.

(c) Attenuation - Cause of attenuation in wave guides, wall current. & derivation of attenuation constant, Q of the wave guide.

(a) Resonantors : Resonant Modes of rectangular and cylindrical cavity resonantors, Q of the cavity resonantors, Excitation techniques, Introduction to Mircostrip and Dielectric resonantors, Frequency meter.

(b) Farrites : Microwave propagation in ferrites, Farady rotatiion, Devices employing Faraday rotation (isolator, Gyrator, Circulator). Introduction to single crystal ferromagnetic resonators, YIG tuned solid state resonators. Microwave tubes : Space charge spreading of an electron beam, Beam focussings. Klystrons : Velocity Modulation, Two Cabvity Klystron, Reflex Klystron Efficiency of Klystrons. Magnetrons : Types & description, ehoeretical relations between Electric & Magnetic field of oscillations. Modes of oscillation & operating characteristics. Travelign wave tubes : O & M type traveling wave tubes. Gyrotorons : Constructions of different Gyrotrons, Field - Particle Interaction in Gyrotron. Microwave Measurement :

(a) Microwave Detectors : Power, Frequency, Attenuation, Impedance Using smith chart, VSWR, Reflectometer, Directivity, Coupling using direction coupler.

(b) Complex permitivity of material & its measurement: definition of complex of solids, liquids and powders using shift of minima method.

 

Atomic, Molecular And Laser Physics  PY-601  

Principles of laser action in atoms and molecules, stimulated emission, emission line shapes and dispersion effects. Techniques for the control of laser output employing Q-switching, mode locking and mode dumping. Optical cavity design and laser stability criteria. Spectra of hydrogen and helium like atoms, fine structure, magnetic dipole interaction and hyper fine structure, Lamb shift (only qualitative treatment). Interaction with external fields: Stark effect, linear Stark effect for hydrogen atom, Zeeman and Paschenback effect, general factors influencing spectral line width and intensities. System with identical particles, action symmetry, the hydrogen molecule, Hitler-London method, electronic, vibrational and rotational spectra of diatomic molecules. Frank-Condon principle, Raman effect. Experimental methods in atomic and molecular physics: FTIR, laser and Raman spectroscopy.

 

Instrumentation Methods And Advanced Analytical Techniques  PY-602  

Signal processing techniques: pre-amplifiers, filters; Measurement techniques: sensors and transducers, general instrumentation, measurement of voltage, current, charge, frequency etc.; Nuclear detection methods: coincidence measurements, voltage and pulse height analyzers, single and multichannel analyzer. Techniques for atomic structure determination: Diffraction methods, Transmission electron microscopy (TEM), low energy electron diffraction (LEED); surface morphology using scanning electron microscopy (SEM), scanning tunneling microscopy (STM) and atomic force microscopy (AFM). Techniques for compositional analysis: electron probe micro analyzer (EPMA) and energy dispersive analysis (EDAX), X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), depth profiling by ion beam sputtering and Secondary ion mass spectrometry (SIMS), Low energy ion scattering (LEIS), Rutherford Back Scattering Spectrometry (RBS), Nuclear reaction analysis (NRA).

 

Solid State Physics  PY-603  

Reciprocal lattice, X-ray, electron and neutron diffraction, lattice vibrations, normal modes, Einstein and Debye models, phonons, thermal conductivity and thermal expansion. Free electron theory, Bloch theorem, energy bands in solids, Tight binding approximation, APW and OPW methods, Fermi surfaces, de Haas van Alphen effect, superconductivity, quantum hall effect, Basics of semiconductor Physics. Dielectric properties and losses, quantum theory of magnetism. Lattice vacancies, Schottky defects, Frenkel defects, diffusion and colour centres, order – disorder transformation, nanostructures and applications.

 

Physics Of Semiconductor Devices  PY-604  

P-n junctions, I-V Characteristics, capacitance, tunnel diode, Schottky barriers, ohmic contacts, heterojunctions, bipolar junction transistors, transistor as an amplifier and a switch, field effect transistors, MOSFET devices, Metal-semiconductors FET, Hetero structure FET, MIS devices, Photonic devices, crystalline and amorphous solar cells, photo detectors, LEDs, Semiconductor Lasers, solid state microwave devices Techniques to measure properties of semiconductors: Four probe method, Hall Effect, spreading resistance for diffusion measurements, measurement of mobility of carriers. Semiconductor device and IC fabrication technology: an overview, epitaxial growth, diffusion, oxidation, wafer doping and etching, photolithographic processing, ion implantation, ultra purification

 

Numerical Methods And Computer Programming PY-605  

Introduction to Computers, Unix operating system, programming basics in C , C++ and Fortran languages. Numerical methods: finite difference calculus, interpolation and extrapolation, roots of equations, solution of simultaneous linear algebraic equations, least squares curve fitting, Monte Carlo simulation for numerical integration, numerical solution of ordinary differential equations, Runga Kuuta method IV order, matrix eigen value problems. Introduction to modeling and simulation: simple examples: particle in a box, random walk problem, Rutherford scattering.

 

M. Sc. Laboratory Work

A consolidated list of Experiments, which are to be performed in I, II and III semester is given below (in each semester there will be a minimum of ten experiments out of the following list, which are to be performed by each student).

Lab I 

• Computer Basics & Programming Lab, Introduction & applications of Internet.

Lab II & Lab III-

• Operational Amplifier
  • Study of Characteristics
  • Applications of operational amplifier
• Digital Electronics:
  • D/A Converter
  • A/D Converter
  • Study of various types of flip-flops.
• Transistor amplifier
  • To study characteristics of direct coupled amplifier and its frequency response.
  • To study true stage R.C. coupled transistor amplifier.
• Oscillator:
  • To study monostable and bistable multivibrator.
  • Study of different types of oscillators:
    • Hartley’s,
    • Colpitt’s,
    • Clapp’s
• Semiconductor/Transistor:
  • To determine hybrid parameters of a transistor
  • To study transistor bias stability with a given power supply
  • Field effect transistor/study of characteristics and FET as an amplifier.
• Microwave:
  • To study the characteristics of reflex klystron and measure SWR and reflex coefficient.
  • To measure dielectric constants of solids and liquids.
• To study the dynamics of a lattice through electrical analog experiments.
• Study of normal modes of a coupled pendulum system and study of oscillations in mixed mode and find the period of energy exchange between the two oscillations.
• To study the magnetic transition and determine the Curie temp. of a given solid.
• Lasers:
  • To study the Gaussian nature of Laser beam: To measure spot size and divergence
  • To study diffraction using laser.
• Fibre optics:
  • To study the characteristics of an optical fibre cable and determine its numerical aperture, threshold energy, slope efficiency and relative output power.
• To verify Bragg’s law of diffraction using microwaves.
• Faraday effect: To determine the magnetic flux density using the axial Hall probe and calculate the verdet’s constant.
• Normal Zeeman Effect
  • Observing the normal Zeeman effect in transverse and longitudinal configuration spectroscopy using a Lummer Gehrcke plate/Fabry Perot Etalon.
  • Measuring the Zeeman split of the red Cadmium line as a function of the magnetic field – spectroscopy using a Lummer - Gehrcke plate/Febry Perot Etalon.
• To study absorption of radioactive particles and determine range using at least two sources.
• To study characteristics of a GM Counter and to study statistical nature of radioactive decay.
• To study spectrum of β – particles using gamma ray spectrometer.
• To calibrate a scintillation spectrometer and determine energy of γ – rays from an unknown
• source.
• 19.
  
  • (a) To study variation of energy resolution for a NaI (Tl) detector.
  • (b) To determine attenuation coefficient (μ) for γ – rays of a given source.
• To study Compton scattering of x-rays and verify the energy shift formula.
• To study Hall effect and to determine Hall Coefficient.
• To analyze energy of electrons using a magnetic spectrometer.
• To study the electron spin resonance using ESR spectrometer.
• To study Meissner Effect and critical temperature of a super conductor.
• To study the characteristics of a vacuum pump and to determine the throughput of a gas.
• To deposit a thin film (Al) and study its characteristics.
• To determine the grain size and particle density of a given specimen by optical microscope.
• To study the oxidation kinetics of given alloy using a microbalance and a furnace (weight gain method).
• To prepare a nanomaterial using sol-gel method and determine the particle size.
• To deposite a thin film of metal using high vacuum coating unit and study to properties (resitivity, optical properties).
• To determine the ultrasonic velocity, compressibility and elastic constants in a solid/liquid using an ultrasonic interferometer.
• To determine the dielectric constant of a dielectric filled in an electric condenser using an audio oscillator and a digital voltmeter.
• Kerr Effect: To study the Kerr effect in a PLZT element.
• To study the phenomenon of Nuclear Magnetic Resonance* using Eartl’s field NMR, * (Spin lattice relaxation and Curie’s law).
• Muon Physics: To measure muon life times and monitor cosmic radiation.
• Optical pumping: To study optical pumping for exploring atomic energy states, atomic transitions and atomic collisions using electromagnetism in the form of light, radio frequency and uniform constant magnetic fields for isotopes of natural rubidium.
• Sonoluminescence: To study the phenomenon of son luminescence i.e. the effect of light from sound.
• Signal Processor Lock in amplifier: To study the detection of weak signal from noise using a lock in amplifier (Phase sensitive detection).
• Computer programming assignments for computer Lab. Work
• To study the variation of resistivity of a given semiconductor with temperature using for probe technique and also determine band gap.
• To study birefringence using Pockel’s effect.
• To carry out the emission and absorption spectroscopy using metal arc spectrometer.
• To record a Frank-Hertz curve for Argon and measure the energy emission of free electrons for inelastic collision.
• To study the current voltage characteristics of a CdS photo-resistor.
• To study the resonance of a driven damped harmonic oscillator and the effect of magnetic damping on shape of resonance curves.
• To measure the magnetic susceptibility of paramagnetic solution by Quinckes method and to find the ionic molecular susceptibility and magnetic moment.
• To study 16-bit addition, subtraction, division on 8086 Microprocessor.
• To study Raman Effect in materials.
• To study the electronic structure of Iodine using spectroscopic methods.