Download document 8913605

Draft Syllabus for BOS approval : M.Sc. Physics ( Credits : 90 )
Semester 1 (Credits :20 =5X4)
Paper
Module
C -DE
C -CV
C -CM
A
B
A
Differential Equations
Complex Analysis and tensor
Classical Mechanics
No. of
classes
24
24
24
C -NLD
B
Nonlinear Dynamics
24
MPHC 4103
C -SP1
C-QM-1
A
B
24
24
50
MPHC 4104
C -SC
C -EC
C -EL
C -IC
A
B
A
B
Statistical Physics I
Quantum Mechanics I and Linear
Algebra
Semiconductor Physics
Electronics and Communication
Core experiments (electronics)
Interfacing & Computer tools
24
24
50
MPHC 4101
MPHC 4102
MPHC 4151
Group
Subject
Marks
50
50
50
250
Semester 2 (Credits :20 =5X4)
Paper
MPHC 4205
MPHC 4206
MPHC 4207
MPHC 4208
MPHC 4252
Module
Group
Subject
C- ED1
C- SR
C- SP2
A
B
A
Electrodynamics I
Special relativity
Statistical Physics II
No. of
classes
24
24
24
S-SSa
B
Solid state physics a
24
C-QMIIa
C-QMIIb
S-AM
S-ED2
C -NEL
C -NT
A
B
A
B
A
B
Quantum mechanics II
Quantum Mechanics III
Atomic and Molecular physics
Electrodynamics II
Core experiments (non electronics)
Numerical Techniques
24
24
24
24
Marks
50
50
50
50
50
250
Semester 3 (Credits :25 =5X5)
Paper
Module
MPHC 4309
C- Gth
S-SSb
S-NE a
A
B
A
Group theory
Solid state physics b
Nuclear Physics
No. of
classes
24
24
24
S-NE b
B
Particle physics
24
General Relativity & Fluid mechanics
24+24
50
Material Physics I & II
Introductory Astrophysics & Cosmology/ Foundation of
Solid State Electronics
Introductory high energy physics/ Semiconductor devices
Core lab ( Communication)
Core lab (Microprocessors)
24+24
24
50
MPHC 4310
MPHE 4301
EL-1
MPHS 4301
EL-2
S1
MPHC 4353
S2
C- COM
C- MIC
Group
A
B
A
B
Subject
Marks
50
50
24
250
1
Semester 4 (Credits :25 =5X5)
Paper
Module
MPHS 4402
MPHS 4403
Group
S3
S4
A
B
S5
A
S6
B
MPHS 4404
S7
MPHS 4451
S8
MPHS 4452
S9
Subject
Stellar Structure & Evolution/ Communication theory
Stellar Atmosphere, Binary Star &ISM/ Digital Signal
processing
QFT & Standard Model/ /VLSI
Astroparticle physics/ Microprocessor and
microcontroller
Computational Physics / Photonics and devices of the
future
Special lab:
Astrophysics/ Electronics
Project
No. of
classes
24
24
Marks
50
24
24
48
50
50
50
50
250
SEMESTER 1
MPHC4101
[24 lectures]
C- DE:
Differential equations, special functions, Green’s functions, Integral Transforms
Differential equations: Theory of second order linear homogeneous differential equation,
Singular points-regular and irregular, Frobenius’ method, Fuchs’ theorem, linear independence
of solutions-Wronskian, second solution, Sturm-Liouville theory, Hermitian operators,
completeness.
Special Functions: Basic properties (recurrence and orthogonality relations, series expansion) of
Bessel, Legendre, Hermite and Laguerre functions.
Inhomogeneous differential equations: Green functions.
Integral Transforms: Fourier and Laplace transforms and their inverse transforms. Bromwich
integral (use of partial fractions in calculating inverse Laplace transforms). Transforms of
derivative and integral of a function. Solution of differential equations using integral transforms.
C- CV:
[24 lectures]
Complex analysis and tensor analysis
Recapitulation: complex numbers, triangular inequalities, Schwarz inequality, Function of a
complex variable – single and multivalued function. Limit and continuity. Diferentiation –
Cauchy-Riemann equations and their applications. Analytic and Harmonic Functions. Complex
integrals. Cauchy’s theorem (elementary proof only), converse of Cauchy’s theorem, Cauchy
integral formula and its corollaries, Series – Taylor and Laurent expansion, classification of
2
singularities, branch point and branch cut, residue theorem and evaluation of some typical
integrals using this theorem.
4D geometry in arbitrary curvilinear coordinates; transformation of tensors, mathematical
operation with tensors (addition, subtraction & multiplication), metric tensors, raising and
lowering of indices, unit tensor, levicivita symbol, invariant volume elements, covariant
differentiation, Christoffel symbol, curvature tensor.
MPHC4102
C- CM:
[24 lectures]
Classical Mechanics
An overview of the Lagrangian formulation: some specific applications of Lagrange’s equation,
small oscillations, normal mode frequencies.
Rigid Bodies: Independent co-ordinates, orthogonal transformations and rotations (finite and
infinitesimal), Euler’s theorem, Euler angles, Inertia tensor and principal axis system, Euler’s
equations, heavy symmetrical top with precession and nutation,
Hamilton’s principle: Calculus of variations, Hamilton’s principle, Lagrange’s equations from
Hamilton’s principle, Legendre transformations and Hamilton’s canonical equations, canonical
equations from a variational principle. Principle of least action.
Canonical transformations: Generating functions, examples of canonical transformations, group
property, integral invariants of Poincare, Lagrange and Poisson brackets, infinitesimal canonical
transformations, conservation theorem in Poisson bracket formalism, Jacobi’s identity, angular
momentum Poisson bracket relations.
Hamilton-Jacobi theory: The Hamilton-Jacobi equation for Hamilton’s principle function, the
harmonic oscillator problem, Hamilton’s characteristic function, Action-angle variables.
Lagrangian formulation for continuous systems: Lagrangeian formulation of acoustic field in
gases, the Hamiltonian formulation for continuous systems, canonical equations from a
variational principle, Poisson brackets and canonical field variables.
C- NLD:
[24 lectures]
Nonlinear Dynamics:
Why Nonlinear Dynamics --The basic differences of Nonlinear Systems with Linear ones-Flows and Maps, Fixed Point Analysis in 1-D Systems, Fixed point analysis and Qualitative
features of Phase Portraits in 2-D systems, Limit Cycles, Generalisation of ideas in higher
dimensions, Bifurcations-- 1-D systems, Bifurcations-- 2-D systems -- mainly local ones with
some notions of Global Bifurctions, Hamiltonian systems- integrability and nonintegrability-onset of chaos in nearly integrable systems, Poincare Section and Maps along with
Stroboscopic Maps , 1-D and 2-D Maps -- Logistic, Standard and Baker's Maps -- Chaos and
Liapunov
3
Exponents, Ideas of strange attractors and chaos – Nonlinear Oscillators, Frcatals and Fractal
dimensions.
MPHC4103
C- SP1:
[24 Lectures]
Statistical Physics I
Introduction : Objective of statistical mechanics, specification of the state of a many particle
system, phase space, counting the number of microstates in phase space, statistical ensemble,
postulate of equal a priori probability, Liouville’s theorem, Ergodic Hypothesis, The H-theorem,
probability calculation, Thermal , Mechanical, General interaction.
Microcanonical ensemble: Thermal interaction between systems in equilibrium, Temperature,
Heat reservoirs, sharpness of the probability distribution, Application.
Canonical ensemble: System in contact with a heat reservoir, Boltzmann distribution,
canonical partition function, calculation of mean values in canonical ensemble, connection with
thermodynamics, Entropy of an ideal gas, Gibb’s paradox, Application.
Grand canonical ensemble: System in contact with a particle reservoir, chemical potential,
grand canonical partition function and grand potential, fluctuation of particle
number, chemical potential of an ideal gas, Application.
C-QM1:
[24 lectures]
Quantum Mechanics I and Linear Algebra
Recapitulation of basic concepts: Wave packet, Gaussian wave packet, Fourier transform,
spreading of a wave packet, Fourier transforms of delta and sine function, co-ordinate and
momentum space: co-ordinate and momentum representation, Parseval’s theorem, eigenvalues
and eigenvectors: Momentum and parity operators, commutativity and simultaneous
eigenfunctions, complete set of eigenfunctions: expansion of wave functions in terms of a
complete set, one dimensional problems: square well potential (E>0), delta function, double delta
potential, application to molecular inversion, multiple potential well, Kronig-Penney model.
Operator method in quantum mechanics: Formulation of quantum mechanics in vector space
language, uncertainty principle for two arbitrary operators, one dimensional harmonic oscillator
by operator method.
Quantum theory of measurement and time evolution: Double Stern-Gerlach experiment for spin
½ systems, Schrodinger, Heisenberg and interaction pictures.
Three dimensional problems: Three dimensional problems in Cartesian and spherical polar coordinates, 3 d well and Fermi energy, radial equation for a free particle and 3 d harmonic
oscillator, eigenvalue of a 3 d harmonic oscillator by series solution.
Angular momentum: Angular momentum algebra, raising and lowering operators, matrix
representation of j = ½ and j = 1, spin, addition of two angular momenta: Clebsch-Gordan coefficients, examples.
4
Approximation methods: Time-independent perturbation theory, first and second order
corrections to the energy eigenvalues, first order correction to the eigenvectors, degenerate
perturbation theory, application to one-electron system – relativistic mass correction, spin-orbit
coupling (LS and jj ), Zeeman effect and Stark effect, Variational method: He atom as an
example, first order perturbation, exchange degeneracy, Ritz principle for excited states for He
atom.
Vector space: Axiomatic definition, linear independence, bases, dimensionality, inner product,
Gram Schmidt orthogonalization.
MPHC4104
C- SC :
Semiconductor Physics
[24 lectures]
Carrier concentration in semiconductors, p-n junction band diagram, I-V and C-V
Characteristics; basic semiconductor equations, depletion and diffusion capacitance, Reverse
Breakdown; Noise; Bipolar Junction Transistors (BJT); Ebers-Moll equation. Frequency
response;
Metal semiconductor junctions: Schottky barriers; Rectifying and ohmic contacts; Tunnel diode;
Uni-junction transistor (UJT); Field Effect Transistor (FET): types, structure, JFET, MESFET,
MOSFET: characteristics, threshold voltage.
C- EC:
Electronics and Communication
[24 lectures]
Analog circuits: Comparators, Multivibrators, Waveform generators: Square wave, triangle wave
and pulse generators. Solid state detectors (Si and HPGe); Measurement of energy and time
using electronic signals from the detectors and associated instrumentation; Multi channel
analyzer.
Introduction to signals; Concepts of Voice & Data Communication; Transmission lines,
Transmission Channels; Modulation & Multiplexing of Analog and Digital Signals; CCITT /
ITU Standards of Voice & Data Communication Systems; Pulse Code Modulation (PCM);
Digital Multiplexing (PDH&SDH).
MPHC4151
C- EL:
Core Experiments (Electronics):
1. Determination of band gap and reverse saturation current of a p n junction diode
2. Construction of Astable Multivibrator and VCO
5
3. To study UJT Characteristics
4. To study Active Filters (High pass, Low pass, Band pass, Notch)
5. To study T Filters (High and Low pass filter)
6. To study Pi Filters (High and Low pass filter)
C- IC:
Introduction to Open Source Computing Tools: Brief inventory, The Linux Comand line
Computing Environment
Data Visualization and Curve fitting using Gnuplot.
Scientific Computing using Python/Numeric/Scipy/Matplotlib: Language essentials,
Computer Interfacing
Principles of Computer interfaced experiments: Sensors, Sampling, ADC width and delay, DAC
limitations, Precision in digitized experiments. Components of the IUAC Phoenix/Expeyes box:
Digital I/O, DAC, PWG, Counter, ADC, Amplifiers. Familiarization with the python API.
Software and Hardware triggers, Hardware control, Data acquiring and analysis using unipolar
and bipolar signals: Fast Vs. Precision experiments, Design / Coding for simple experiments
using available thermo/mechanical/audio sensors.
SEMESTER 2
MPHC4205
C -EDI:
Electrodynamics I
[24 lectures]
Electrostatics and Magnetostatics: Scalar and vector potentials, gauge transformations, multipole
expansion of (i) scalar potential and energy due to a static charge distribution, (ii) vector
potential due to a stationary current distribution, electrostatic and magnetostatic energy,
Poynting’s theorem, Maxwell’s stress tensor.
Radiation from time dependent sources of charges and currents: Inhomogeneous wave equations
and their solutions, Radiation from localized sources and multipole expansion in the radiation
zone.
Relativistic electrodynamics: Equation of motion in an electromagnetic field, electromagnetic
field tensor, covariance of Maxwell’s equations, Maxwell’s equations as equations of motion,
Lorentz transformation law for the electromagnetic fields and the fields due to a point charge in
uniform motion, field invariants, covariance of Lorentz force equation and the equation of
motion of a charged particle in an electromagnetic field, the generalized momentum, energy-
6
momentum tensor and the conservation laws for the electromagnetic field, relativistic Lagrangian
and Hamiltonian of a charged particle in an electromagnetic field.
C- SR:
Special Relativity
[24 lectures]
Lorentz transformations, four- vectors, tensors, transformation properties, metric tensor, raising
and lowering of indices, contraction, symmetric and antisymmetric tensors, four dimensional
velocity and acceleration, four- momentum and four-force, covariant equations of motion,
relativistic kinematics (decay and elastic scattering), Lagrangian and Hamiltonian of relativistic
particles.
MPHC4206
C- SP2:
Statistical Physics II
[24 lectures]
Quantum statistical mechanics: Quantum-mechanical ensemble theory: the density matrix,
Quantum Liouville’s theorem, density matrices for microcanonical, canonical, grand canonical
ensemble, simple examples of density matrices- one electron in a magnetic field, particle in a
box.
Systems composed of indistinguishable particles- BE and FD distributions.
Ideal Bose and Fermi gas: statistics of occupation number, equation of state,
BE condensation, Thermodynamic behavior of ideal Bose gas, black-body radiation,
Thermodynamic behavior of ideal Fermi gas, the electron gas in metals, statistical
equilibrium of white dwarf stars.
S-SSa
[24 lectures]
Solid State a
Band theory of solids: Bloch equation, empty band, nearly free electron bands, band gap, number
of states in a band, tight binding method, effective mass of an electron in a band, concept of
holes,
Lattice dynamics: Classical theory of lattice vibrations under harmonic approximation, vibrations
of linear monatomic and diatomic lattices, acoustical and optical modes, long wavelength limit,
optical properties of ionic crystal in the infrared region, adiabatic approximation (qualitative
discussion), normal modes and phonons, inelastic scattering of neutron by phonon, lattice heat
capacity, models of Debye and Einstein, comparison with electronic heat capacity, anharmonic
effects in crystals - thermal expansion and thermal conductivity, Mossbauer effect.
Dielectric properties of solids: Static dielectric constant, electronic and ionic polarization of
molecules, orientational polarization, static dielectric constant of gases, Lorentz internal field,
static dielectric constant of solids, complex dielectric constant and dielectric losses, relaxation
time, classical theory of electronic polarization and optical absorption, ferroelecticity – case of
BaTiO3.
7
Magnetic properties of solids: Origin of magnetism, Diamagnetism, Quantum theory of atomic
diamagnetism, Landau diamagnetism (qualitative discussion), Paramagnetism, classical and
quantum theory of paramagnetism, case of rare-earth and iron- group ions, quenching of orbital
angular momentum, Van- Vleck paramagnetism and Pauli paramagnetism, Ferromagnetism:
Curie-Weiss law, temperature dependence of saturation magnetization, Heisenberg’s exchange
interaction, ferromagnetic domains, ferrimagnetism and antiferromagnetism.
MPHC4207
C-QM2A:
[24 lectures]
Quantum Mechanics II
Density matrix: Basic definition and some properties.
Introduction to Mean Field Theory: Basic concepts, independent particle model, first quantized
Hartree method.
Time-dependent perturbation theory: Time dependent perturbation theory, interaction picture,
constant and harmonic perturbation – Fermi’s Golden rule, sudden and adiabatic approximation.
Scattering theory: Laboratory and centre of mass frames, differential and total scattering crosssection, scattering amplitude, scattering amplitude, scattering by spherically symmetric
potentials, partial wave analysis and phase shifts, Ramsauer Townsend effect, relation between
sign of phase shift and attractive or repulsive nature of the potential, scattering by a rigid sphere
and square well, Coulomb scattering, formal theory of scattering – Green’s function in scattering
theory, Lippman-Schwinger equation, Born approximation.
Symmetries in quantum mechanics: Conservation laws and degeneracy associated with
symmetries, continuous symmetries – space and time translations, rotations, rotation group,
homomorphism between SO(3) and SU(2), explicit matrix representation of generators for j = ½
and j = 1, rotation matrices, irreducible spherical tensor operators, Wigner-Eckart theorem,
discrete symmetries – parity and time reversal.
Identical Particles: Meaning of identity and consequences, symmetric and antisymmetric
wavefunctions, Slater determinant, symmetric and antisymmetric spin wavefunctions of two
identical particles, collisions of identical particles.
C-QM2B:
[24 lectures]
Relativistic quantum mechanics: Klein- Gordon equation, Feynman- Stuckelberg interpretation
of negative energy states and concept of antiparticles, Dirac equation, covariant form, adjoint
equation, plane wave solution and momentum space spinors, spin and magnetic moment of the
electron, non-relativistic reduction, helicity and chirality, properties of gamma matrices, charge
conjugation, normalization and completeness of spinors, Lorentz covariance of the Dirac
equation, bilinear covariants and their transformation under parity and infinitesimal Lorentz
transformation, Weyl representation and chirality projection operators.
Field quantization: Basic ideas, construction of conjugate momentum from Lagrangian density,
commutation relations for bosonic and anticommutation relations for fermionic fields in terms of
8
field and momentum or creation and annihilation operators, quantization of Klein-Gordon and
electromagnetic fields, ides of Fock space and occupation number representation.
MPHC4208
S-AM:
Atomic and Molecular Physics
[12 Lectures]
Review of Quantum Mechanics and Perturbation theory , Short Introduction on direct product
space (in order to facilitate a proper understanding of addition of angular momenta, L-S
coupling, j-j coupling etc.), One electron atom : Solving the eigenvalue problem of the
Hamiltonian: Energy levels and Bound States, Interaction of one-electron atoms with
electromagnetic radiation: Setting up the Hamiltonian, Transition rates, Absorption and
Emission, Zeeman Effect , Fine structure of hydrogenic atoms: Energy corrections, Fine
structure splitting , Many electron atoms: Central field approximation, Slater determinant,
electronic configurations- shells, subshells, degeneracies, periodic table. L-S coupling, Hund's
Rules, j-j coupling.
[12 lectures]
Molecular Electronic states: concepts of molecular potential, separation of electronic and nuclear
wave functions, born- Oppenheimer approximation, electronic cells of diatomic molecules,
electronic angular momenta, approximation methods for the calculation of electronic
wavefunctions, LCAO approacvh, states for hydrogen molecular ion, Coulomb exchange and
overlap integral, symmetries of electronic wavefunctions, shapes of molecular orbital, pi and
sigma bond, term symbol for simple molecules.
(5)
Rotation and vibration Molecules: Solution of nuclear equation, molecular rotation, non rigid
rotator, centrifugal distortion, symmetric top molecules, molecular vibrations, Harmonic
oscillator and anharmonic oscillator approximation, Morse potential.
(3)
Spectra of diatomic molecules: Transition matrix element, vibration-rotation spectra, pure
vibrational transition, pure rotational transitions, vibration-rotation transitions, electronic
transitions: structure, Franck-Condon Principle, rotational structure of electronic transitions,
Fortrat diagram, dissociation energy of molecules, continuous spectra, Raman transitions and
Raman spectra.
(4)
EL-EDII:
[24 Lectures]
Plasma Physics: Definition of plasma, its occurrence in nature. Basic Plasma Phenomena,
Dimensionless parameters, plasma frequency, quasi neutrality, Debye shielding, Plasma
generation.
(5)
Single particle motions in constant and slowly time varying electric and magnetic fields and non
uniform magnetic fields. Magnetic bottle and loss cone.
(5)
9
Radiation from moving point charges: Lienard-Wiechert potentials, fields due to a charge
moving with uniform velocity, field due to an accelerated charge, radiation at low vwlocity,
Larmor’s formula and its relativistic generalization, radiation when velocity (relativistic) and
acceleration are parallel, Brehmstrahlung, radiation when velocity and acceleration are
perpendicular, synchrotron radiation, Cherenkov radiation (qualitative treatment only), Thomson
and Compton scattering.
Radiation reaction: Radiation reaction from energy conservation, Problem with AbrahamLorentz formula, limitations of CED.(10)
MPHC4252
C- NEL:
1. Determination of Planck’s constant
2. To Study Michelson’s Interferometer
3. Franck Hertz Experiment.
4. Study of Iodine Spectra
5. ESR.
C- NT :
Numerical and graphics libraries, text processing. Case Studies: Motion under classical force
fields, Random walk problem, Dynamical systems.
Implementation of Numerical algorithms using Fortran 90: Descriptive statistics, Solution of
linear systems, root finding, interpolation and least square polymonial approximation, Numerical
Integration, ODES: Euler and RK45, Uses of the random number module.
SEMESTER 3
MPHC4309
C- Gth:
Group Theory
[24 lectures]
Symmetries, representation theory, broad overview of finite and continuous groups, rotation
group, the nature of time-reversal and space-inversion operations, point groups and crydtal
tensors, application to X-ray analysis of structures and molecular vibrations, the Wigner-Eckart
theorem, Lie groups and representations, Young tableaux, Dynkin diagrams, SU(2), Gauge
invariance, equivalence with angular momentum. SU(3) and quarks.
C-SSb:
10
Solid State Physics
[24 lectures].
Solid State b
Crystallography: Review of fundamental ideas, crystal class, point group and space group,
common crystal structures, reciprocal lattice and Brillouin zone, Bragg-Laue formulation of Xray diffraction by a crystal, atomic and crystal structure factors, experimental methods of X-ray
diffraction: Laue, rotating crystal and powder method, electron and neutron diffraction by
crystals (qualitative discussion). Band structures in copper, GaAs and silicon, classification of
metal, semiconductor and insulator, topology of Fermi surface, cyclotron resonance – de HaasVan Alphen effect, Boltzmann transport equation – relaxation time approximation, Sommerfeld
theory of electrical conductivity.
Magnetic resonances: Nuclear magnetic resonances, Bloch equation, longitudinal and transverse
relaxation time, hyperfine field, electron spin resonance.
Imperfections in solids and optical properties: Frenkel and Schottky defects, defects in growth of
crystals, the role of dislocations in plastic deformation and crystal growth, colour centres and
photoconductivity, luminescence and phosphors, allos – order-disorder phenomena, BraggWilliams theory, extra-specific heat.
Superconductivity: Phenomenological description of superconductivity, Meissner effect, type-I
and type-II superconductors, heat capacity, energy gap and isotope effect, BCS theoryexpression for energy gap , ac and dc Josephson effect, hich-Tc superconductors (qualitative).
MPHC4310
S-NE :
[24 lectures]
Nuclear and Particle Physics
Nuclear Properties: Nuclear size, Rutherford scattering, nuclear radius and charge distribution,
nuclear form factor, mass and binding energy, angular momentum, parity and symmetry,
magnetic dipole moment and electrical quadrupole moment, experimental determination, Rabi’s
method.
Two-body state: Properties of deuteron, Schrodinger equation and its solution for ground state of
deuteron, rms radius, spin dependence of nuclear forces, electromagnetic moment and magnetic
dipole moment of deuteron and the necessity of tensor forces.
Two-body scattering: Experimental n-p scattering data, partial wave analysis and phase shifts,
scattering length, magnitude of scattering length and strength of scattering, significance of the
sign of scattering length, scattering from molecular hydrogen and determination of singlet and
triplet scattering lengths, effective range theory, low energy p-p scattering, nature of nuclear
forces: charge independence, charge symmetry and isospin invariance of nuclear forces.
β-decay: β emission and electron capture, Fermi’s theory of allowed β decay, selection rules for
Fermi and Gamow-Teller transitions, parity non-conservation and Wu’s experiment.
11
Nuclear structure: Liquid drop model, Bethe-Weizsacker binding energy/mass formula, Fermi
model, Shell model and collective model.
Nuclear reactions and Fission: Different types of reactions, quantum mechanical theory,
resonance scattering and reactions – Breit-Wigner dispersion relation, compound nucleus
formation and break-up, statistical theory of nuclear reactions and evaporation probability,
optical model, principle of detailed balance, transfer reactions, nuclear fission: experimental
features, spontaneous fission, liquid drop model, barrier penetration, statistical model, superheavy nuclei.
Nuclear Astrophysics: (Qualitative ideas only), nucleosynthesis and abundance of elements,
neutron star.
Particle Physics:
[24 lectures]
Symmetries and conservation laws, Hadron classification by isospinand hypercharge, SU(2) and
SU(3): Groups, algebras and generators, Young tableaux rules for SU(2) and SU(3), quarks,
colour, elementary ideas about electroweak interaction and the Standard Model.
MPHE4301
EL-MP:
[24 + 24 lectures]
Material Physics I
Materials Physics: Overview of materials: crystalline and amorphous materials, glasses,
semiconductors, compound semiconductors, solar energy materials, luminescent and
optoelectronic materials, polymer, liquid crystals, ceramics, classification according to bonding –
Pauling and Phillips theories. (5)
Synthesis and preparation of materials: single crystal growth, zone refining, doping elements of
elemental and compound semiconductors, growth of thin films, PVD and CVD processes,
principles of polymer processing, preparation of ceramic powders, mechanical and chemical
methods.(5)
Epitaxy: Theoretical growth models FM,VW and SK, molecular beam epitaxy (MBE),
metalorganic vapour phase epitaxy (MOVPE) (6)
Characterization of materials: Defects and nanostructures; diffraction technuiques;X ray
diffraction structure determination;from XRD data; Neutron diffraction; Thermal methods :
DTA, TGA, DSC; microscopy:TEM, SEM; Optical spectroscopy:UV and IR; Nuclear
techniques: NMR, ESR, Mossbauer and positron annihilation. Heat treatments, quenching and
annealing, radiation damage. (8)
Material Physics II
12
Phase transition in materials: thermodynamics and phase diagrams, statistical theories of phase
transitions, critical phenomenon, calculation of critical exponents, van der waals and
ferromagnets; diffusion in solids; variation of diffusion constant with temperature.(6)
Mechanical properties: Deformation and fracture. (2)
Electrical properties of alloys, ceramics, conducting polymer: resistivity variation of materials at
low and high temperatures, Kondo effect; Effect of pressure on resisitivity.(3)
Magnetic properties of different materials. (3)
Glasses: Definitions, theories of glass transition, tunneling states. (3)
Exotic solids and nanomaterials: Quasicrystal; Principles of quantum size effect and its
applications; Penrose lattices and their extentions in 3 dimensions; synthesis of nanostructures
and materials; Characterization methods; special carbon solids: fullerenes and carbon
nanotubule.(7)
EL-GT:
[24 Lectures]
General Relativity: The equivalence principle, non-inertial frames and non-Euclidean geometry,
general co-ordinate transformations and the general covariance of physical laws, commutator
and Lie derivative, equation for geodesic deviation, energy-momentum tensor and conservation
laws, Einstein equations, Hilbert’s variational principle, gravitational energy-momentum
pseudotensor, Newtonian approximation, linearized field equations, gravitational waves,
gravitational radiation, static spherically symmetric spacetime, Schwarzchild’s exterior solution,
motion of perihelion of mercury, bending of light, gravitational redshift, radar echo delay.
Fluid Mechanics
MPHS4301
SPL-AP1:
[24 lectures]
Introductory Astrophysics and Cosmology:
Overview of Astrophysics and Cosmology: Interpretation of the difference and nature in which
modern astronomy and astrophysics are related; how astrophysics and cosmology are essentially
interlinked and yet different in their aproaches; historic milestones in the development modern
astrophysics and cosmology; different scales and orders of magnitued in astrophysics and
cosmology: mass, length and time; electromagnetic spectrum and multiwavelength astronomy;
some exemplary problems and applications of physical laws in astrophysics and cosmology.
Introduction: Celestial co-ordinates and celestial times;photometry and magnitude scales;
extinction, local thermodynamics, characteristic temperature in astrophysics.
Cosmology: Homogeneity and isotropy of the universe: explanation and examples to illustarte
the concept; expansion and Hubble's law: mathematical derivation of Hubble's law using
13
homogeneity and isotropy, comparison of scales to illustrate effects of expansion on celestial
objects; particles in the universe; Newtonian dynamics of the universe: scale factor, physical
distance and co-moving distance, Friedmann equation and Fluid equation, acceleration equation;
solutions of the Friedmann equation: evolution of the universe; Observational parameters:
Hubble constant, density parameter, deceleration parameter; Cosmological constant and
evolution of the universe.
SPL-SSE1:
Foundations of Solid State Electronics :
[24 lectures]
Density of states, Fermi-Dirac statistics, intrinsic and extrinsic carrier densities, free electron
theory, mobility and diffusion constant, Einstein relation, temperature dependence of mobility,
negative differential mobility, Boltzmann transport equation, magnetotransport – Hall effect and
magnetoresistance, Thermoelectric power. Quantum Hall effect; space charge in semiconductors,
relaxation effects, ambipolar effects; experimental determination of mobility, diffusion constant
and lifetime of minority carriers – Haynes- Shockley experiment. Electron -hole pair
recombination, Shockley-Hall-Read statistics, kinetics of traps and recombination centres,
surface states - pinning of Fermi level; Noise, continuity equations,
SPL-AP2:
[24 lectures]
Quantum Field Theory:
Hadron structure: elastic e-p scattering, electromagnetic form factors, electron-hadron DIS,
structure functions, scaling, sum rules, neutrino production.
Strong interactions: QCD, asymptotic freedom, gluons and jets in e+ - e-→hadrons, scaling
violations.
Low energy weak interactions: Fermi theory, calculation of decay widths of muon and π+.
Neutrino physics: Theory of two-flavour oscillation, solar and atmospheric neutrino anomalies,
neutrino experiments. Indian neutrino observatory.
Dimensional reasoning using natural units, Lorentz invariance, Feynman – Stuckelberg approach
to relativistic scattering process, early exposure to the diagrammatic method using interacting
scalar ABC fields. Classical fields, Symmetries and Noether's Theorem, Free quantum fields.
SPL-SSE2:
Semiconductor Devices (MOS and CCD)
[24 lectures]
14
MOSFET and CCD : Surface charge and C-V characteristics of MIS ; device characteristics,
Non-equilibrium conditions, linear and saturation regions, sub-threshold region, mobility,
temperature dependence, threshold shift, short channel effects, FAMOS, VMOS; types of
MOSFET. Fabrication of MOS – implantation, oxidation, metallisation, etching, lithography,
contacts.
Charge coupled devices (CCD); interface trapped charge, charge storage, basic CCD structure,
surface and buried channel CCD; charge storage and frequency response, IRCCD.
MPHC4353
C- COM:
Communication Expts
1.
2.
3.
4.
5.
6.
7.
Pulse Width Modulation and Demodulation
Study of Frequency Modulation and its Demodulation using IC PLL565
Pulse Position Modulation and Demodulation
Study of Amplitude Shift Keying and Demodulation
Study of Frequency Shift keying and Demodulation [IC 8038 Function Generator used]
Study of Amplitude Modulation and Demodulation [IC Version 1496]
C- MIC :
Microprocessors
Microprocessor (8085)
•
•
•
•
•
•
•
Succinct understanding of architecture
Instruction set
Introduction to SIM8085
Programs related to
o Data block copy in forward, reverse, partial reverse
o Arithmetic operations – 8 bit, 16 bits, multibyte
o Code generation
o String Operation
Input – Output data through port
Interfacing with 8255 PPI
o LED
o 7 – Segment display
Delay routine
o Calculation of execution time
o Application of delay to data input – output
15
SEMESTER 4
MPHS4402
SPL-AP3
[24 lectures]
Stellar structure and evolution: Stellar spectral classification: observed Hertzsprung-Russell
diagram, physical basis of the classification; stellar atmospheres: applications of radiation
transfer, plane parallel atmosphere, grey atmosphere, Eddington approximation and formation of
spectral lines; laying down the stellar structure equations, a discussion on the boundary
conditions; virial theorem and stellar energy sources: short discussion on stellar nucleosynthesis
and reaction rates basic assumptions for model bulding; polytropic stellar model and a
comparison with real main sequence stars, Chandrasekhar mass, Standard model; convection in
stars and stability; theory of main sequence (MS) stars: homologous model, eddington
luminosity limit: radiative stability, evolution of low and high mass MS stars; late stages of
stellar evolution; end stages of stars as a function of mass.
Binay stars: Classification of Binary stars; mass determination using Visual Binaries; Eclipsing
and Spectroscopic Binaries.
Interstellar medium and star formation: Interstellar dust and gas; formation of proto-stars; premain sequence evolution; stars, brown dwarfs and planets; initial mass function.
Galaxies: Normal galaxies: morphological classification, physical characteristics and kinematics.
SPL-SSE3 :
[24 Lectures]
Communication theory
A: Random signals and noise: probability, random variables, probability density function,
autocorrelation, power spectral density. Analogue communication systems: amplitude and angle
modulation and demodulation systems, spectral analysis of these operations, super heterodyne
receivers; elements of hardware, realizations of analogue communication systems; signal-tonoise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM)
for low noise conditions. Fundamentals of information theory and channel capacity theorem.
B. Synchronous Digital Hierarchy (SDH).Data over SDH.Electromagnetic waves, Multipath
Radio Wave Propagation Models .Spectrum Issues. Concepts of 2nd & 3rd Generation of cellular
Mobile Systems.
16
C. Microwave Science &Technology: Sources-Klystrons, Magnetrons TWT., Solid State
Microwave Devices. Cavities, Q factor; waveguides, strip line, micro strip, attenuators, isolators,
directional couplers. Microwave Monolithic Integrated circuits (MMIC).
SPL-AP4:
[24 lectures]
Stellar atmosphere
Thermonuclear reactions: reaction rates, low energy behavior and astrophysical S-factors,
forward and reverse reactions, resonant and nonresonant reactions, Maxwell-Boltzmann
distribution of velocities, Gamow peak. Big Bang nucleosythesis: He production, Be bottleneck,
abundance of light elements. Stellar structure: classical stars, degenerate stars. Nuclear burning
in stars: H burning, He burning, advanced nuclear burning, core collapse. Stellar
nucleosynthesis: abundance of elements, production of nuclei, r-,s- and γ-processes.
SPL-SSE4:
Digital Signal Processing:
[24 Lectures]
Fundamentals of discrete time system: Basic definitions, important sequence, Linear and time
invariant systems, impulse response, shifting, convolution, Linear constant coefficients
difference equations, FIR, IIR systems. Frequency domain analysis:Fourier transform of
sequences, properties, Inverse F.T., sampling of continuous time signal, Sample and Hold
amplifiers, Nyquist rate and aliasing problem, interpolation formula, frequency response of
rectangular window, recovery of analog signal. Discrete Fourier Transform: DFT and its
computation, properties, circular and linear convolution, FFT, Time and frequency decimination,
IDFT, Interpretation of DFT results, DFT-FT relationship. Z-transform : Z-transform, properties,
calculation of IZT, Application to the solution of difference equations, System function of a
digital filter.
MPHS4403
SPL-AP5 :
[24 lectures]
Standard Model of elementary particles:
Fermions and bosons: the spin-statistics theorem; Supersymmetry, The fundamental
interactions: Boson Exchange, The boson coupling to Fermions, Weak and Electromagnetic
interactions, Gravitational Interaction. The Quark Gluon Plasma. Cross Sections:
Examples of elementary particle processes in the early universe. Decays and
resonances. Relevant decay kinematics.
Parity violation in weak interactions, Helicity and helicity conservation,
Charge conjugation invariance, Gauge transformations and gauge invariance,
Superstrings. Gauge invariance in Electroweak theory. The Higgs mechanism
17
of spontaneous symmetry breaking. Running couplings. Parton model
to QCD. Testing the standard model. Vaccum Structure in Gauge theories.CPT
theorem and CP and T symmetry. CP violation.
Gauge Invariance in QM, Lie groups and algebras, Lorentz group, Spinor and Vector fields,
Fields in interaction. Renormalization: Elementary treatment.
SPL-SSE5:
VLSI:
[24 Lectures]
VLSI design flow. Switch level RC delay models. CMOS technologies.
Layout design rules. Circuit characterization and performance estimation: Delay estimation.
Logical effort and transistor sizing. Power dissipation. Interconnect design margin. Reliability.
Scaling. Circuit simulation : CMOS Design and Layout : Analog MOS circuits: Sub-circuits –
switch, diode, current sinks and sources, current mirrors. Amplifiers - inverters, differential
amplifiers. Digital MOS circuits: CMOS combinational logic gates, multiplexers, latches and
flip-flops. Device and circuit characterization. Interconnect simulation. Modelling and Synthesis
with the Verilog HDL, Digital System Design, Electronic Design Automation Tools. Ultrafast
GaAs digital and linear ICs,
SPL AP6:
[24 lectures]
Astroparticle Physics
Astroparticle physics in perspective: Relationship to High Energy Physics. Astrophysics and
Cosmology.
Elementary particle processes in galactic, intergalactic and atmospheric production and
transmissions, Physics of particle and radiation detection, Acceleration mechanisms in sunspots,
supernovae shocks and accreting binaries. Primary cosmic rays: Charged and uncharged
components: neutrino, gamma, xray and gravitational wave astronomy, Secondary cosmic rays:
Atmospheric propagation, cosmic rays at the sea level and underground, Extensive air showers.
Review of cosmological principles, Thermodynamics of the early universe, Thermal history of
the first three minutes: BBN and CMBR. Problems leading to the formulation of Inflation:
horizon, flatness and monopole problems and their resolution through the mechanism of
inflation. Dark Matter: Motivation and Possible candidates. Open questions in Astroparticle
physics.
SPL-SSE6 :
Microprocessors and microcontrollers
[24 lectures]
Microprocessors: Introduction to microcomputers - memory-I/O interfacing devices. 8085 CPU;
Architecture BUS timings, Demultiplexing the address bus generating control signals, instruction
18
set, addressing modes, illustrative programs, writing assembly language programs: looping,
counting and indexing-counters and timing delays; stack and subroutine; extension to 8086 CPU.
–(10)
Interfacing chips – special purpose and general purpose interfacing chips, Microprocessor
applications. (6)
Microcontrollers: Introduction to microcontrollers –8051, Assembly language programming with
microcontrollers (8)
SPL-AP7:
[48 lectures]
Computational Astrophyics
Semester 3:
Introduction to Matlab as a tool for numerical and symbolic computation: Basic matlab tools,
matrix manipulation, writing functions, random numbers.
i. Numerical computing using matlab: Interpolation, root finding of non-linear equations, curvefitting tools, numerical differentiation and integration, ode solvers (with examples) and
numerical solution of PDEs.
ii. Random walks in 2-dimensions and 3-dimensions.
iii. Two body problems.
Semester 4:
Astrophysical and Cosmological modeling:
i. Stellar models: Solving the Lane-Emden equations numerically with polytropic equation of
state (with different polytropic indices) with special case being of white dwarfs.
ii. Studying the evolution of the universe: Solving the Friedmann equations numerically and
finding the scale of distances and age of the universe for different models with current
cosmological parameters.
Data Analysis
i. Studying the Hubble's law of expansion of the universe using simulated data set for galaxies.
ii. Analysing SNIa data to determine the deceleration parameter and the Hubble parameter of the
universe.
iii. Application of Image analysis techniques and FFT in Astrophysics.
SPL-SSE7:
19
Photonics:
[24 + 24 = 48 lectures]
LED: materials, isoelectronic traps, radiative and non-radiative centres, efficiency,
heterojunction LED, frequency response; organic LEDs. Diode lasers: optical confinement, gain
and threshold condition , Fabry- Perot cavity; DHJ and quantum well lasers; high power lasers;
quantum cascade lasers; Modulators - Franz-Keldysh effect. Photonic crystals.
Photodetectors: thermal vs quantum, Schottky, PIN and Avalanche Photodiodes (APD);
Quantum Well IR photodetectors (QWIP). Solar cells: bulk, thin film; Si, GaAs, CIGS, CdTe,
and organic cells
Semiconductor Devices (Nanomaterials and Nanoscale Devices):
Physics of nanomaterials, types of nanostructures – quantum size effect - quantum wells, wires
and dots ; variation of density of states,, preparation of nanomaterials – top down, bottom up
methods , self - assembled monolayers. Determination of particle size from TEM, XRD and
light scattering. Secondary Ion Mass Spectrometry (SIMS), Fullerene, CNT – Physics &
Technology.
MPHS4453
SPL-AP8 : Astrophysics –
1. To estimate the temperatures of an artificial star by photometry.
2. To study the solar limb-darkening effect.
3. To study effective temperature of stars by B-V photometry.
4. To determine the solar constant using the principle of calorimetry.
5. To study the Fraunhofer absorption lines from the solar photosphere.
6. To study the Hubble’s law and to determine Hubble’s constant using SN1a data and galaxy
spectra (from CLEA).
SPL-SSE8 : Solid State Electronics –
[1] Microcontroller 8051
[2] Experiments based on Digital Signal Processing : MATLAB
[3] Experiments with standard PCM Kits : Sampling, Quantization & Coding & Multiplexing of
multiple PCM Signals
[4] Using MATLAB (Student Version) for the simulations of Digital Transmissions via Modulations
- PAM, QAM, FSK & Synchronisation in Digital Communications.
[5] Digital & Analog communication
[6] To study A/D & D/A Conversion
[7]SPICE simulation of Analog MOS circuits
[8] Study of comparator
[9] Fiber Optics Experiment
20
[10] Magneto-resistance and Hall coefficient
[11] Mobility of semiconductor
MPHS4454
Project
21