Goa University Courses

M.Sc. (Physics)

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Duration: 2 Years

Eligibility: Graduation

Course Structure

Course Code	Course Title
Semester – I
PHC101	Mathematical Physics
PHC102	Classical mechanics
PHC103	Electromagnetic Theory
PHC104	Electronics Practicals
PHC105	Computer Programming Laboratory
Semester - II
PHC106	Quantum Mechanics – I
PHC107	Basic Electronics
PHC108	Statistical Mechanics
PHC109	General Physics Practicals
semester - III
PHC201	Quantum Mechanics – II
PHC202	Nuclear and Elementary Particle Physics
PHC203	Solid State Physics
PHC204	Solid State Physics Practicals
PHC205	Seminars
	Summer Fellowships  Extra Credit
Semester - IV
PHO302	Neutron Physics
PHO303	Superconductivity
PHO304	X-ray Spectroscopy
PHO305	Electronics Practicals - II
PHO306	Semiconductor Physics
PHO307	Projects
Remote Sensing (Marine Science Department)

 

Course Detail

Semester - I

PHC 101 : Mathematical Physics

Ordinary Differential Equations

Second order homogeneous and inhomogeneous equation, Wronskian, General Solutions, Ordinary and Singular points, Series Solutions.

Special Functions

Legendre's equation, Generating function for the Legendre Polynomial, Roddgues's Formula, Recurrence Relations, Spherical Harmonies, Bessel Equation, Generating Function, Recurrence Relations, Spherical Bessel Function, Hermite Equation, Generating Function, Recurrence Relations

Functions of Complex Variable

Limits, Continuity, Analyticity of Functions of a Complex Variable, Taylor and Laurent Series, Isolated and Essential Singuladties, Branch Cuts, Cauchy Formula, Contour Integration, Application of Residue Theorem, Analytical Continuation, Asymptotic Series and Methods of Steepest Descent

Linear Vector Spaces

Linear Operators, Matrices, Coordinate Transformations, Eigenvalue Problems, Diagonalization of Matrices, Infinite Dimensional Spaces, Elements of Group Theory.

Integral Transforms

Fourier Series, Fourier Transforms, Laplace Transforms, Applications of Integral Transforms

Boundary Value and Initial Value Problems

Fourier Series in two and three Variables, Coupled Pendulums, Vibrating String in one Dimension, Heat Conduction, Wave Equation, Introduction to Green Function Method.

 

PHC 102 : Classical Mechanics

Newton’s Laws of Motion

Mechanics of a single particle, Mechanics of a system particles, Constraints and their classification, Principle of virtual work, D’Alembert’s principle.

Lagrangian Formulation

Degrees of Freedom, Generalized Coordinates, Calculus of variations, Hamilton’s principle, Euler-Lagrange’s equations of motion, Application to non-holonomics systems, Advantages of a variation principle formulation, Conservation theorems and symmetry properties.

Rigid Body Dynamics

Eulerian angles, Inertia tensor, Angular momentum of rigid body. Free motion of rigid body, Motion of symmetric top.

Hamilton’s equation of motion

Legendre transformation and the Hamilton equations of motion, cyclic coordinates and conservation theorems, Routh’s procedure and oscillation about steady motion, Derivation of Hamilton’s equations from a variational principle, Principle of least action.

Canonical Transformations

Equations of canonical transformations, Examples of canonical transformations, Poisson brackets and other canonical invariants, Equations of motion, Infinitesimal canonical transformation theorems in Poisson bracket formulation, Angular momentum, Poisson brackets relations, Lagrange brackets.

Hamilton - Jacobi Theory

H - J equation for Hamilton's principal function, Harmonic oscillator problems, H -J equation for characteristic function, Action angle, Kepler’s problem.

Two-body Central Force Problem

Equations of motion and first integrals, Classification of orbits, virial theorem, Differential equation and integrable power law potentials, Kepler’s problem.

Small Oscillations

Simple Harmonic Oscillations, Damped Oscillations, Forced Oscillations without and with damping, Coupled Oscillations.

 

PHC 103 : Electromagnetic Theory

Maxwells Equations

Displacement current, Maxwell’s equations, Vector and Scalar potentials, Gauge transformation, Lorentz and Coulomb gauge, Poynting’s theorem, Conservation of energy and momentum for charged particles and fields

Electromagnetic Waves

Plane electromagnetic waves and their propagation in non-conducting and conducting media, Frequency dispersion in conductors, Dielectrics and plasma

Electromagnetic Radiation

Retarded Potentials, Fields and radiation by localized dipole, Lienerd Weichert potentials, Power radiated by an accelerated charge.

Physics of Plasmas

Electrical neutrality in a plasma, Particle orbits and drift motion in a plasma, Magnetic mirrors, The hydro-magnetic equations, The pinch effect, Plasma oscillations and wave motion, Reflection from a plasma (ionosphere).

Wave Guides

Propagation of Waves between conduction planes, Wave guides in arbitrary crosssection, Wave -guides in Rectangular Cross-section, Coaxial Wave guide, Resonant Cavities, Dielectric wave guides.

Relativistic Electrodynamics

Lorentz transformation as four dimensional orthogonal transformation, Lorentz matrix, four vectors in mechanics and electrodynamics, Lorentz covariance of Maxwell equations, field tensor, transformation of fields, field due to a point charge in uniform motion, relativistic Lagrangian formulation of classical mechanics and electrodynamics.

 

PHC 104 : Electronics Practicals

(Minimum 10 Experiments)

• Operational Amplifier parameters
• Series voltage regulator using transistors
• Constant Current Supply
• Schmitt trigger circuit and its use as zero crossing detector and squaring circuit (2 experiments)
• J.K. flip-flop counter: Scale of 16 and 10 using IC
• Adder and Subtracter Circuits (2 experiments)
• Oscillators: Design and Construction of Wien bridge
• Oscillators: Design and Construction of phase shift oscillators
• Multivibrators : Design and Construction of Monostable (2 experiments)
• Multivibrators : Design and Construction of Astable (2 experiments)

 

PHC 105 : Computer Programming With C

Introductory Concepts:

Introduction to computers, Introduction to Linux OS, Linux basics, Introduction to C, Writing a C Program, Compiling and Executing the Program, Error Diagnostics, Some

simple C Programs, Desirable Program Characteristics.

C Fundamentals:

The C character Set, Identifiers and Keywords, Data types, Constants, variable and Arrays, Declarations, Expressions, Statements, Symbolic Constants

Operators and Expressions:

Arithmetic Operators, Unary Operators, Relational Logical Operators, Assignment Operators, the Conditional Operators, Library Functions.

Data Input and Output:

Preliminaries, Single character input and output, entering Input data, writing output data, Opening and closing data file, format statements.

Control Statements:

Preliminaries, Branching statements, Looping statements, nested control structure, switch, break, continue, go to statements.

Functions:

Defining functions, accessing functions, Passing arguments to a function.

Arrays:

Defining an array, processing an array, passing arrays to functions, multidimensional arrays.

 

Semester - II

PHC 106 : Quantum Mechanics – I

Schrodinger's Equation and Hermitian operators

(a) Time -dependent Schrodinger equation, continuity equation, expectation values, Ehrenfest's theorems, time-independent Schrodinger equation and stationary states.

(b) Hermitian operators, eigenvalues and eigenstates of Hermitian operators, momentum eigenfunctions, orthogonality and completeness of wave functions, Computability and compatibility of observables, parity operation.

Exactly Solvable Problems

(a) One-dimensional square-well problem, bound states, One dimensional potential step and potential barrier, Scattering states, linear harmonic oscillator.

(b) Spherically symmetric potential, orbital angular momentum operator L, eigenvalues and eigenfunctions of L' , Spherical harmonics, hydrogen atom problem.

Vector space formulation of quantum mechanics

Dirac Notation, representation of states and observables, bra and ket vectors, linear operators, relation with wave mechanics, algebra of hermitian operators, matrix representation, unitary operators, Schrodinger and Heisenberg representations, linear harmonic oscillator problem by operator method.

Angular Momentum theory

Angular momentum and rotation, Rotational Symmetry and conservation of angular momentum, Treatment of general angular momentum by operator method, eigenvalues and eigenvectors, Eigen values and eigenfunctions of L2 and Lz operators, ladder operators L+ and L- , spin angular momentum, algebra of Pauli matrices, Pauli representation of angular momentum operators. Addition of two angular momenta, spin-orbit interaction, Clebsch Gordon coefficients,. Central forces with an example of hydrogen atom. motion of electron in a magnetic field

 

PHC 107 : Basic Electronics

Network Analysis and Synthesis

Superposition theorem, Maximum power transfer theorem, T and _ networks, Lattice Network, Symmetric Network, Network in the frequency domain, transform impedance, Network functions for the one port and two port, poles and zeros of network function, Positive real functions, Hurwitz polynomials, Synthesis of one port networks, Foster and Cauer forms.

Small Signal Amplifiers

Transistor h - parameters, Graphical determination of h - parameters, Small signal model of BJT (analysis of multistage amplifiers) and FET Amplifiers and analysis, Transistor amplifier with Re unbypasssed, High Ri amplifier circuits, Miller’s Theorem and Bootstrapped CC amplifier.

Power Amplifiers

Large signal amplifiers, Class of operation, Harmonic distortion, class A amplifier with resistive and transformer coupled load, Power efficiency calculations, class B amplifiers, crossover distortion, Complementary symmetry amplifiers.

Communication Electronics

(a) Fundamentals of amplitude, frequency & phase modulation, Simple circuits for amplitude modulation and Demodulation, Digital PCM and Demodulation, Fundamentals of optical communication,

(b) Definition of microwave, characteristic features, application of microwaves Microwave Oscillators: Klystron, reflex klystron, magnetron, Gun diode, Cavity resonators, standing wave detectors

 

PHC 108 : Statistical Mechanics

Kinetic Theory and Equilibrium state of Dilute Gas

Formulation of problem, binary collisions, Boltzmann transport equation, Boltzmann’s H theorem, Maxwell-Boltzmann distribution, Method of the most probable distribution, analysis of the H theorem, recurrence and reversal paradoxes, Validity of the Boltzmann transport equation

Classical Statistical Mechanics

Review of laws of thermodynamics, Entropy, Thermodynamic Potentials, Postulate of Classical Statistical Mechanics, Microcanonical ensemble, derivation of thermodynamics, equipartition theorem, Classical ideal gas, Gibbs paradox

Canonical and Grand Canonical Ensembles

Canonical ensemble, energy fluctuations in canonical ensemble, grand canonical ensemble, density fluctuations in grand canonical ensembles, equivalence of canonical and grand canonical ensembles, behaviour of W(N), meaning of Maxwell construction

Quantum Statistical Mechanics

Postulates of quantum statistical mechanics, density matrix, ensembles in quantum mechanics, third law of thermodynamics, ideal gases in microcanonical and grand canonical ensembles, foundations of statistical mechanics

Ideal Fermi Gas

Equation of state of Ideal Fermi Gas, theory of white dwarfs, Landau diamagnetism, DeHass-Van Alphen effect, Pauli paramagnetism

Ideal Bose Gas

Photons, phonons, Bose-Einstein condensation

 The Ising Model

Definition of the Ising model, Equivalence of the Ising model to other models, Spontaneous magnetization, The one dimensional Ising model, Formulation of the two dimensional ising model, The Onsager solution

Critical Phenomena

The order parameter, the correlation function and the fluctuation dissipation theorem, critical exponents

 

PHC 109 : General Physics Practicals

• Types of Statistical Distributions
• Forbidden Energy gap of a Germanium/Silicon and a light emitting diode
• Analysis of Sodium Spectrum – Quantum defect and Effective quantum number
• Michelson Interferometer / Fabry-Perot Interferometer
• Determination of Stephan's Constant
• Zeeman's effect
• Frank Hertz Experiment
• Statistical Distribution of radioactive decay
• Verification of Inverse Square Law using GM counter
• Linear Absorption Coefficient of Aluminium using GM counter
• Debye Relaxation
• Thermal diffusivity of Brass
• Calibration of Lock-in Amplifier
• Mutual inductance lock-in amplifier
• X-ray Emission
• Strain Gauge
• Ultrasonic Interferometer
• Thermometry – Calibration of temperature sensors like diode, thermocouple with respect to platinum resistor

 

Extra 1-Credit Course : Summer Fellowships

Students are to be encouraged to attend summer fellowships offered by various national laboratories, institutes and universities during the summer months of May and June each  year between Parts I and II. The learning cum experience gained at such places will be required to be written up as a report and presented. These will be assessed by the D.C. and awarded a grade. Such fellowships may be considered to be equivalent to ONE credit. This extra credit will be in addition to the 80 credits that are necessary for the award of a Master’s degree in Physics.

 

Semester - III

PHC 201: Quantum Mechanics II

1. Identical Particles

Symmetrization postulate, connection between spin and statistics, Pauli exclusion principle, wave function for fermions and bosons. Examples : Helium atom, Scattering of identical particles

2. Perturbation Theory

Time - independent perturbation theory, non-degenerate and degenerate cases, applications to simple problems, time dependent perturbation theory, Golden rule for transition probability, application to simple problems.

3. Variational method

Upper bounds on the ground state and excited state energies, applications to simple problems.

4. Scattering Theory

Schrodinger equation for a free particle in three dimensions, expansion of plane waves in spherical harmonics, scattering by a potential, scattering amplitude and cross-sections, Born approximation, scattering by Yukawa and Coulomb potentials, concept of phase shifts, calculation of phase shifts from potentials, partial wave expansion of scattering amplitude, optic & theorem

5. Relativistic Wave Equations

A. Klein-Gordon equation, Plane wave solution, charge and current densities, hydrogen atom.

B. Dirac equation, algebra of Dirac matrices, covariance of Dirac equation, plane wave solutions, equation in an electromagnetic field,

C Properties of Dirac electron The spin of the Dirac particle, Magnetic dipole moment of electron, Velocity operator, Expectation value of the velocity.

D Parity, Charge conjugation and time reversal operations Parity operation, Charge conjugation, a time reversal operation.

E Feynmann’s theory of Positrons

 

PHC 202 : Nuclear Physics

Basic Properties of Nuclei

Nuclear mass, charge and radius, Nuclear spin, Parity Statistics, magnetic and electric quadrupole moments

Nuclear Models

a) Liquid Drop model, Weizsacker's mass formula, mass parabolas

b) Nuclear shell model. Energy levels in a three dimensional harmonic oscillator well potential, spin orbit interaction, prediction of magic numbers, ground state spins and parities, magnetic moments, Schmidt lines, Nuclear quadrupole moments

c) Collective Model, Bohr-Mottelson theory of surface vibrations and rotations of nuclei, Excitation spectra of deformed nuclei, Niisson model

Nuclear Transformations

a) Alpha decay, Barrier penetration problem. Gamow's theory of Alpha decay, Geiger- Nuttal law, Alpha spectra and nuclear energy levels

b) Gama transitions, multipole radiations, Quantum theory of the transition probability, selection rules, Angular correlation, Calculations of transition rates and comparison with experiments, internal conversion

c) Beta Decay, Experiments in beta spectra, neutrino hypothesis, Fermi's theory of beta decay, Kurie plots, ft values, Allowed and forbidden transitions, selection rules, electron capture, parity violation in beta decay, experimental verification, measurement of neutrino helicity

Two-Body Problem

Properties of deuteron Theory of the ground state of deuteron, Magnetic moment and electric quadrupole moment of deuteron, tensor force, theory of nucleon-nucleon scattering at low energy, phase shift and scattering length , effective range theory, experimental determination of low energy parameters, nature of nuclear forces, Wigner, Heisenberg and Majorana exchange forces, Mason theory of nuclear force

Nuclear Reactions

Cross-sections, principles of detailed balance, Bohrs theory of compound nucleus, resonances and Breit-Wigner Single level formulation, optical model, Direct reaction, Nuclear fission

Elementary Particles

Classification of elementary particles, Baryons, Mesons and Leptons, Strong , weak and electromagnetic interactions, Isobaric spin, strangeness and parity, elementary particles reactions and decays, Resonances, Eightfold way, Quark model

 

PHC 203 : Solid State Physics

Crystal structure and Crystal Binding (scope C. Kittel and Ashcroft and Mermin)

Crystals - Lattice, Bravais lattice, primitive unit cell , seven crystal systems, fourteen Bravais lattices, definitions of directions, coordinates and planes, Simple crystal structures: NaCl, CsCl, diamond, hexagonal close-packed structure, cubic ZnS structure, Reciprocal Lattice - Diffraction of waves by crystals, Bragg law, Scattered wave amplitude - Fourier analysis, reciprocal lattice vectors, diffraction conditions, Laue equations, Brillouin zones, Geometric structure factor, Atomic Structure factor Point Defects General Thermodynamic Features, Color centres, Line Defects: Dislocations Crystals of inert gases - Van der Waals - London interaction, repulsive interaction,  equilibrium lattice constants, cohesive energy, Ionic Crystals - Electrostatic or Madelung Energy, evaluation of Madelung constant, covalent crystals, bonding in metals, and Hydrogen bonds

Free Electron Theory and Energy Bands in solids (scope M. A. Omar)

Free electron theory - Sommerfield model, Electrical conductivity, Experimental electrical resistivity of metals, Heat capacity of electron gas, Experimental heat capacity, Thermal conductivity of metals, motion in magnetic fields Cyclotron frequency, Hall effect, AC conductivity,  Energy Spectra in atoms, molecules and solids, Energy Bands in Solids; the Bloch Theorem, Band symmetry in k-space; Brillouin Zones, Number of states in the band, The nearly free electron model, The energy gap and the Bragg reflection, Tight binding model, Metals, insulators and semiconductors, density of states, The Fermi surface, Velocity of Bloch electron, Electron dynamics in an electric field, The dynamical effective mass, Physical origin of effective mass, The hole, Electrical conductivity, Electron dynamics in a magnetic field; cyclotron resonance and Hall effect, Experimental methods of determination of band structure, Limit of band theory; metal-insulator transition

Thermal Properties (scope C. Kittel)

Vibrations of a one -dimensional monatomic lattice, first Brillouin zone, group velocity, long wavelength limit, derivation of force constant from experiment. Vibrations of a one dimensional diatomic lattice. Quantization of elastic waves, phonon momentum, Inelastic scattering by Phonons Phonon Heat capacity, Planck distribution, normal mode enumeration, density of states in one dimension, density of states in three dimensions Debye model for density of states, Debye T' law, Einstein model of the density of states, Thermal conductivity - Thermal resistivity of phonon gas, Umklapp process

Optical and Dielectric Properties (scope C. Kittel) [8+2]

Optical reflectance, Excitons, Raman effect in crystals Macroscopic electric field, local electric field at atom, dielectric constant and polarizability, Structural Phase transitions, Ferroelectric Crystals and Displacive transitions

Magnetic Properties (scope C. Kittel)

Langevin Diamagnetism Equation, Quantum Theory of Diamagnetism, Paramagnetism, Quantum Theory of Paramagnetism, Paramagnetic Susceptibility of Conduction electrons, Ferromagnetic Order, Magnon, Ferrimagnetic Order, Antiferromagnetism, Ferromagnetic Domains

Superconductivity (scope C. Kittel)

Experimental surve- Occurrence of Superconductivity, Destruction of superconductivity by magnetic fields, Meissner effect, Heat capacity, Energy gap, microwave and infrared properties, Isotope Effect Theoretical Survey - Thermodynamics of the transition, London equation, Coherence length, BCS theory, Flux quantization, Type II superconductors, Tunneling, Josephson effects High Tc superconductivity - Introduction (scope : Kittel's book)

 

PHC 204: Solid State Prysics Practicals

• X-Ray Diffraction : XRD of Cubic Material; Powder Pattern and its qualitative and quantitative analysis.
• Determination of Resistivity and Band Gap of a Semiconductor by Four Probe Method
• Measurement of Thermoelectric Power
• Determination of Magnetic Susceptibility and Magnetic Moment of a Paramagnetic Material by Gouy's Method
• Determination of Magnetic Susceptibility and Magnetic Moment of a Paramagnetic Liquid by Quinke's Method
• Study of Hysteresis of a Ferrite and determination of Curic / Ne'el temperature of a Ring made up of a Ferrite Material.
• Determination of Lande's Splitting Factor, g, in an organic radical . ESR Spectrum
• Study of Elastic behaviour of solids using a composite piezoelectric oscillator
• Determination of Transition Temperature of a Ferroelectric Material Dielectric Constant
• Measurement of Activation Energy of F-Centres in Alkali Halide Crystals Thermoluminescence
• Determination of a Hall Coefficient and Nature of a Semiconductor and Mobility of Charge Carriers
• Frequency dependence of Dielectric constant
• Energy band gap of material by UV refluctance.
• IR spectra of material and its analysis.
• Temperature variation of resistivity of semiconductor material and determination of activation energy.
• Raman effect – demonstration applied to a particular material.

Note : A minimum of 12 experiments are expected to be done by the students.

 

PHC 205 : Physics Seminars

This 2 Credit course will consist of 15 weeks of seminars delivered by students, each giving 2 talks of duration 40 minutes each including time for questions and answers. Preparation for each talk will be done in consultation and guidance by a faculty member who would be designated for each student and who will help the student in preparing a synopsis of the talk. Assessment will be done by designated faculty members during the talks. A record will be kept of each talk.

 

Semester - IV

PHO 302 : Neutron Physics

I. Interaction of Neutrons with Matter:

Interaction of neutrons with matter, cross-section and variation with neutron energy. Neutron flux. Maxwellian distribution. Fissile and fertile materials. Chain reaction and neutron life cycle. Fermi four factor formula keff.

II. Neutron Diffusion:

Diffusion theory approximation, derivation of diffusion equation. Neutron balance and  critical equation. Boundary conditions and extrapolation distance. Diffusion length and its measurement.

III. Slowing down of Neutrons:

Slowing down length, lethargy, slowing down in a mixture. Moderations. Slowing down models.

IV. Calculation of Critical Size of Reactors:

Critical equation. One group model, four factor formula and calculation of parameters. Critical size of sphere and cylinder. Effect of reflector.

V. Power Operation:

Reactor kinetics, mean neutron lifetime. The "In-Hour" equation and stable reactor period. Reactivity changes due to temperature. Fission product poisoning . Fuel burn-up. Measurement or reactor power and period.

VI. Reactor Types and Economics:

Descriptions of MAGNOX, CANDU, fast reactor. Calculation of total generation cost. Comparison with economics of oil fired plant. Influence of economics on nuclear plant design.

VII. Radiological Protection:

Units of radiation and radioactivity. Concept and derivation of safe working levels. Monitoring instruments and methods.

VIII. Reactor Fuels and Materials:

Uranium resources and requirements. Isotope separation. (one method). Fuel reprocessing. Storage and disposal of nuclear waste – consideration of different methods.

IX. Nuclear Policy:

Elements of India’s Nuclear Policy. Examples of Policy of other countries.

 

PHO 303: Superconductivity

I. Basic Experimental Aspects :

Zero electrical resistance , Meissner effect , diamagnetic susceptibility , heat Capacity, optical absorption by superconductor, entropy change, thermal Conductivity, destruction of superconductivity by external magnetic fields, London penetration length, Pippard coherence length superconducting behaviour under high pressures, flux quantization, Josephson tunnelling.

II. Superconducting Materials :

Elemental superconductors, superconducting, compounds and alloys, A 15 compounds Chevrel phase compounds, Type 1 and Type 11 materials, high temperature superconductors La-Ba-Cu-0, Y-Ba-Cu-0, Bi-Sr-Ca-Cu-0, Ti-Sr-Ca-Cu-0 and new systems and their crystal structure, experimental studies on the new materials.

III. Theoretical aspects :

Isotope effect, BCS theory, role of electrons and phonons, application of electron bandstructure results to calculate electron - phonon coupling constant, MeMillan's formula, GLAG theory, new mechanisms, recent theories on high Tc materials, expressions for critical temperature Tc, critical field Hc - heavy fermion superconductivity.

IV. Physical Properties and Possible Mechanisms of high Tc Superconductors:

Carrier density, mobility'and effective mass of carriers, magnetic suspectibility in nonsuperconducting and superconducting states , thermal conductivity measurements, spin correlations in the superconducting state, neutron diffraction experiments, tunnelling conductance, energy gap measurements.

Isotope effect in copper-bearing and copper-less oxide superconductors, the possible role of phonons in high Tc superconductivity, the Resonance valence Bond (RVB) theory, charge excitations induced mechanisms, the role of excitons, bipolarons, plasmons etc.

V. Possible Applications of new high Tc Superconductors:

Small current applications microelectronics, IR detectors, neuromagnetics imaging, ultra high frequency generators and detectors , Large Scale/large current applications in the form of bulk and wires : power generation, transmission and storage, magnetically levitated trains, controlled fusion, electric cars - Magnetic applications such as magnetic separations - Other applications like SQUIDS, bolometers, etc.

 

PHO 304 : X-Ray Spectroscopy

Production of X-rays [12+3]

Nature of X-rays, Continuous X-Rays – polarization, frequency spectrum and spacial distribution, Bremsstrahlung in other processes, Characteristic X-Rays – line emission, Mosley Laws, Selection Rules, Nomenclature of X-ray lines, Ratio of continuous and characteristic X-rays, Synchrotron Radiation – Properties, Radiated Power, Spectral and angular distribution, Polarization, pulsed time structure, brightness and emittance, 2. Scattering of X-Rays

Thomson and Rayleigh (Coherent) Scattering, Incoherent (Compton) Scattering, XRay Raman and Plasmon Scattering, X-ray Diffraction and powder analysis techniques

Photoelectron Spectroscopy Photoelectric Effect, Quantum Theory of the Photoelectric Effect, Born Approximation, Shake-up Structure, Experimental Systems, Auger Effect and its Relation to ESCA and X-Ray Spectra, Basic Theory of the Auger, Effect, Detection of Auger Electrons, X-Ray Line Width, Satellites, Low-Energy Satellites, Fluorescence, Measurement of Fluorescence Yield, Autoionization and Internal Conversions

Chemical Shifts in Emission Spectra

Chemical Shifts of Emission Lines, Level Shift, X-Ray Line Shift, Appearance Potential Spectroscopy, Resonance X-Ray Emission Spectroscopy, Width and Fine Structure of Emission Lines, Anisotropic X-Ray Emission Lines, Nuclear Finite-Size Effects

Absorption Spectra

Absorption Edge, Nature of the Absorption Spectrum and the White Line, White Line, X-Ray Absorption Main Edge Structure, Chemical Shifts of Absorption Edges, X-Ray Absorption Near Edge Structure, Extended X-Ray Absorption Fine Structure,  History of EXAFS, Basic Theory of EXAFS, EXAFS Experiment and Form, Data Analysis

X-ray spectrometers: Cauchois type bent crystal X-ray spectrograph, Johnson and  Johansson spectrometes and two crystal x-ray spectrometers

 

PHO 305 : Electronics Practicals - II

• Study of R-S, D/T, J-K Flip-Flops.
• Study of counters: Ripple, Mode 3, Mode 5, Mod 7, Mod 9, Mod 12 counters.
• Study of Shift Register.
• Study of Binary weighted and R-2R D/A Converter.
• Study of Random Access Memory (RAM) Read Only Memory. (ROM)
• Study of A/D Converter.
• Experiment with Microprocessor
• Convert BCD in to HEXADECIMPL
• Design and construction Analog Multiplexer
• Design and construction of Sample and Hold Circuits
• Full adder and subtractor
• Solving of Differential Equation by analog computation using OPAMPS
• Design and construction of Amplitude modulation and Demodulation Circuit.
• Design and construction of frequency modulation and demodulation Circuit.
• Design and construction of variable voltage (0-25V; 1Amp ) Regulated power Supply.
• Design and construction of low voltage SMS power supply.

Any eight experiments to be completed

PHO 306 : Semiconductor Physics

Electrons in Solids 10L

Schrodinger equation for electrons; the free electron problem. filling of electronics states: statistics. Cubic lattices, Diamond and zinc blende structures. Metal, Semiconductors and insulators; Fermi levels in metals and semiconductors.

Electrons in Semiconductors 10L

Electrons in a periodic potential, Bandstructures of Ge, Si and GaAs, Mobile carriers: Intrinsic carriers, intrinsic concentration,Doping: Donors and acceptors; carriers in doped semiconductors.

Carrier Dynamics in Semiconductors 20 L

Scattering in semiconductors; Velocity-electric field relations, Very high field transport: breakdown phenamena, Carrier transport by diffusion; Transport by drift and diffusion, Einstein relation, Charge injection and quasi-Femi levels; Charge generation recombination; Optical processes in semiconductors, Nonradiative Recombination, Continuity equation: diffusion length.

Junctions in Semiconductors : P-N Diodes (20 L)

Unbiased P-N junction., P-N junction under bias., The real diode : consequences of defect, High voltage effects in diodes, Modulation and Switching : AC response.

 

PHO 307 : Projects

This 8-Credit project is to be carried out over semesters 3 and 4 on experimental or theoretical studies that are done by a student in consultation and guidance of a faculty member. The work may be done either in the Physics Department or in a designated laboratory with the permission of the D.C. A comprehensive report is to be written and presentation made to the D.C. in the fourth semester. The assessment is as per the appropriate ordinance of Goa University.