1.
M.Sc (Applied Physics)
M. Sc (Previous)
1.
Mathematical Physics (PH 501)
Complex
Variables
Branch points, Branch lines, Multivalued function, Derivative of complex
function, Analyticity, Analytic function, Cauchy- Riemann equations,
construction of a complex function, singular points, Couchy’s integral theorem,
Couchy’s integral formula, Derivative of a Analytic function, singularities of
an analytic function, Evaluation of definite integrals.
Tensors
Introduction, Covarient and Contravariant tensors, Indicial and
summation convention, Dummy and real indices, Kronecker delta symbol, Tensors of
higher ranks, Algebric operations of tensors, Fundamental tensors, Tensors form
of gradient, Divergence, Laplacian and curl, Divergence of a tensors, Tensors in
Elasticity.
Vectors & Matrices Orthogonal curvililinier coordinates, Lineare Vector space, Linear
independeance and Dependance of vectors, Basis and expansion theorem, Inner –
product and unitary space.Special types of matrices, Hermition and skew
Hermition matrices, Orthogonal unitary matrices, Eigen values, Eigen Vectors,
Caley Hamilton theorem, characteristic of matrix, Trace of matrix.
Special Function Bessel, Legender, Hermite, Laguerre’s, Differential Equations and Polynomials,
Gauss Hyper geometriv and Confluent
Hyper geometric functions.
Integral Transforms Laplace
transforms, Convolution first and second shifting theorem, Inverse Laplace
transform by partial fraction, LT of derivatives.Fourier series. FS of arbitrary period, fourier integral and transforms,
Applications of laplace
transforms to the initial and boundary value problems.
Dirac Delta and Greens Functions Dirac Delta function, derivative of Dirac Delta functions, Greens functions,
Three dimensional Green’s functions, Greens’s functions for Laplace
and Poission’s equations. Green’s functions for wave equations.
Books
-
Mathematics for Engineers & Physicist- L.A.Pipes and L.R.Harvill.
-
Mathematical methods for Physics by G. Arfken.
-
Theoritical Physics vol. I & II – P.M. Morse and H. Feschback.
- Special
Functions by W.W. Bell.
- Methods of
Mathematical physics by R.Courant and D. Hilbert.
-
Mathematical for Physics by Mary I, Boas.
-
Mathematical methods by P.K. Chattopadhyay.
2.
Classical & Statistical Mechanics (PH-502)
CLASSICAL MECHANICS
Lagrangian formulation Generalized co-ordinates, D’Alembert’s principle and
Lagrange’s equation of motion, Velocity – dependent potentials and Rayleigh’s
dissipation function, Simple applications of the Lagrangian formulation.Hamilton’s principle, some techniques of calculus of
variations, Derivation of Lagrange’s equation from Hamilton’s principle,
Extension of Hamilton’s principle to non- holonomic systems, Conservation
properties.
The
Hamilton’s equations of motion
Legendre transformation and the
Hamilton’s equation of motion, cyclic co-ordinates and conservation theorems, Derivation of
Hamilton’s equations from a variational principle, The principle of least
action. The equation of canonical transformation, Poisson
brackets and other canonical invariants, Equations of motion, Infinitesimal
canonical transformations and conservation theorems in the Poisson bracket
formulation, The angular momentum Poisson bracket relations.
Hamilton Jacobi Theory
The Hamilton Jacobi equation for
Hamilton’s principal function, The harmonic oscillator .Problem, The Hamilton Jacobi equation for
Hamilton’s characteristic function, action angle variable
Small Oscillation
Types of oscillations, Small oscillations using
generalized coordinates, Normal modes and normal coordinates, Normal modes and normal co-ordinates, Coupled
pendulum, Triatomic molecule and particles on a string.
Rigid Body Motion
ansformation from space fixed axis to body fixed
axis, Euler’s equations of motion, coriolis force, Moment of inertia tensor.
STATISTICAL MECHANICS
Basic Concepts
Statistical formulation of the mechanical problem,
Macroscopic and microscopic states, Phase space, Concept of ensembles, Postulate
of equal a priori probability, Behavior of density of states, Density
distribution in phase space, Liouville’s theorem, statistical equilibrium,
Distribution of energy between macroscopic systems, approach to thermal
equilibrium, Entropy and its properties, Virial theorem.
Classical Stastical Mechanics
Microcanonical ensemble, Canonical ensemble and Grand
canonical ensemble, Calculation of mean values and fluctuations, properties of
partition function, Thermodynamical variables in terms of partition function,
ideal gas , Gibb’s paradox, The equipartitian theorem and its applications,
Paramagnatism, law of atmosphere, Maxwell’s velocity distribution, Calculation
of average, r.m.s. and most probable speed.
Quantum Statistical Mechanics
Quantum distribution functions (Bose Einstein & Fermi
Dirac), Boltzmann limit for Bosons and Fermions, partition function for ideal
gas, Equation of state, Partition function for diatomic molecule.
Ideal Bose System
Photon gas, Specific heat from lattice vibrations,
Bose-Einstein condensation.
Ideal Fermi System
Fermi energy, Mean energy of Fermions at T = 0 K,
Fermi gas in metals, Fermi energy as a
function of the temperature, Electronic specific heat, Compressibility.
Books:
1.
E.S.R.Gopal -
Statistical Physics 2.
Patharia -
Statistical Mechanics
3.
L.D.Landau &
I.M.Lifshitz -
Statistical Mechanics
4.
Goldstein - Classical Mechanics
5.
Reif – Statistical
Physics
3.
Quantum Mechanics
(PH-503)
Introduction to Quantum Mechanics
Historical development of Quantum Mechanics, Fundamental concepts: Uncertainty
principle, wave function, Schrödinger equation, eigen value and eigen functions.
One dimensional potential problems, spherically symmetric cases, application to
Simple harmonic oscillator and Hydrogen atom.
General Formalism of Quantum Mechanics
Representation of states and dynamical variables and observables, Hermitian
operators, completeness and closure property, commutability, commuting
observables, simultaneous diagonalization of commuting operators, commutator
algebra, Dirac bra and ket notations, matrix representation of an operator,
change of basis, unitary transformation and projection operator, Equation of
motion, Schrödinger, Heisenberg and interaction pictures.
Angular Momentum
Parity or space inversion, rigid rotator as application of parity operator,
rotation operators, angular momentum, eigen values and eigen functions of L2
and Lz operators, ladder operators, Pauli theory of spins, spin polarisation,
addition of angular momentum, computation of Clebsh-Gordon coefficients.
Identical Particles & Spin
Physical meaning of identity, symmetric and anti-symmetric wave functions,
construction from unsymmetrized functions, The Pauli’s exclusion principle.
Approximate Methods
Variational method, application to harmonic oscillator and helium atom (two
electron system), time–independent perturbation theory non-degenerate and
degenerate cases, Stark effect, time dependent perturbation theory, harmonic
perturbation, transition probability, Fermi’s Golden
rule.
Books
1. Powell & Crasemann: - Introduction to Quantum Mechanics
2. Schiff: - Quantum Mechanics
3. Raims:-Wave Mechanics
4. E. Merzbacher: - Quantum Mechanics
5. A.Messiah:- Quantum Mechanics
6. B. K. Agarwal and Hari Prakash- Quantum Mechanics
7. Eisberg- Quantum Mechanics
4.
Atomic & Molecular Physics
(PH-504)
Hydrogen atom gross structures
Schrödinger’s equation, stationary states, solution of Schrödinger's equation
for Coulomb field, quantum numbers n,
l, m, comparison with Bogr's model, the hydrogen spectrum.
The Hydrogen atom fine structure : Electron spin, Stern-Gerlach experiment, the
interaction terms, relativistic correction, spin-orbit interaction, vector
model, spectroscopic terms and selection rules, lamb shift, summary of the
hydrogen spectrum.
Two electron system
Electrostatic interaction and exchange degeneracy, ground and excited states of
helium. Electron spin functions and Pauli's exclusion principle, periodic table.
The central field approximation; the central field. Thomas Fermi-potential, The
gross structure of alkalis atoms.
Angular problems in many electron atoms
The L-S coupling approximation, allowed terms in L-S coupling, fine structure in
L-S coupling, J-J coupling, hyperfine structures, Interaction with external
field: Zeeman, Paschen-Back and Stark effects.
Observed molecular spectra and their representation by Empirical formula
Spectra in visible and ultraviolet regions, spectra in the infrared region,
Radio frequency spectra, Raman spectra.
Interpretation of Infrared and Raman Spectra
Interpretation of the Principle features of infrared and Raman spectra by means
of the models of the Rigid Rotator and of the harmonic oscillator,
interpretation of the line details of infrared and Raman spectra by means of the
models of an harmonic oscillator. Non rigid rotator vibrating rotator and
symmetric top, Intensities in rotation-vibration spectra, symmetry properties of
rotational levels.
Electronic states and Electronic transitions
Electronic energy and total energy, vibrational sructures of electronic
transitions, rotational structures of electronic bands, intensity distribution
in the vibrational structure, Frank-Condon principle.
Lasers
Spontaneous and stimulated emission , optical pumping, population inversion,
coherence ( temporal and spatial) , three level-four level system, optical
resonators, CO2 a nd He-Ne lasers and Excimer laser.
Books:
1. G. K. Woodgate : Elementary Atomic Sturucture, Mc Graw Hill
2. H. S. Mani : Introduction to
Modern Physics, East West Press
3. G. Herzberg : Molecular Spectra
4. C. N. Banwell : Fundamentals of Molecular Spectroscopy
5. W. Demtroder : Laser Spectroscopy
6. O. Sevelto : Principle of Lasers
7. K. Shunoda : Introduction to Laser Physics
8. H. E. White : Introduction to Atomic Spectra
5.
Solid
State
Physics (PH-505)
X-ray Diffraction
Laue derivation of scattered wave (Laue condition), Diffraction condition in
terms of reciprocal lattice vector, Introduction to Crystal Structure, Structure
factor for a basis, Atomic from factor, Calculation of structure factor for BCC,
FCC and Diamond Structure.
Phonons and Lattice Vibration
Vibrations of a monoatomic lattice (concept of Brillouin zone should be
introduced) Vibration of a diatomic lattice, Acoustic and optical modes of
vibration, Quantization of lattice vibration, Phonons, phonon momentum, Lattice
heat capacity( Einstein and Debye models), Inelastic scattering of neutrons by
phonons, Anharmonic crystal interaction , Thermal conductivity and resistivity.
Crystal Binding
Types of solids; Vander Waal’s solid, Ionic and covalent solids, metals,
semiconductors; intrinsic and extrinsic semiconductors, Law of mass action,
Electron and hole mobilities, impurity levels, p-n junction.
Free Electron Theory
Sommerefeld free electron theory of metals, Energy level and density of states
in one and three dimensions, Chemical potential of a free electron gas, Heat
capacity of free electron gas, DC and AC electrical conductivity of metals,
Plasmons-transverse and longitudinal modes, Transparency of metals in UV region,
Widemann-Franz law, Failure of free electron theory of metals.
Band Theory of Solids Nearly free electron theory, Origin of energy gap, Electron in a periodic
potential, Bloch function and theorem (with proof), Properties of Bloch
function, No. of allowed states in a band, reduced zone scheme, Extended Zone
Scheme, Repeated (periodic) zone scheme, Crystal momentum.
Diamagnetism and Paramagnetism
Classical Theory of Diamagnetism, Langvin theory of paramagnetism, Quantum
theory of paramagnetism, Paramagnetic susceptibility of conduction electrons.
Ferromagnetism, Anti Ferromagnetism and Ferrimagnetism
Ferromagnetism-Wiess theory, Curie point, Exchange integral, Saturation
magnetization and its temperature dependence, Saturation magnetization at absolute zero, Ferromagnetic
domain, anisotropic energy, Transition region between domains concept of Bloch wall), Spin waves (magnons),
Thermal excitation of magnons, Magnetic properties of rare ions and iron group
ions, Crystal field splitting, Quenching of angular momentum, Antiferromagnetism
- Neel temperature, Anti ferromagnetic magnons, Ferrimagnetism-Ferrimagnetic
order.
Superconductivity
Electrical and magnetic properties of superconductor, Occurrence of
superconductivity, Meissner effect, Heat capacity, Energy gap, Microwave
properties, isotope effect, type I, II superconductors, thermodynamics of
superconductivity, London equation, London penetration depth, Coherence length,
Outlines of BCS theory, Flux Quantization in a superconducting ring, New super
conducting materials.
Books: 1. Introduction to Solid Sate Physics: C.Kittel (John Wiley and Sons)
2. Solid
State Physics: N.W. Ashcroft and Mermin
(Saunders college, Philadelphia:CBS
publishing Asia Ltd.)
3. Solid
State Physics: C.M. Kachhava (Tata Mc Graw-Hill
publishing Company, New Delhi)
4. Solid
State Physics: Adrianus J. Dekker (Mac Millan )
5. Solid
State Physics: Ibach and H.Luth (Springer
Verlag, Berlin 1990)
6. Introductory Solid
State Physics: H.P.Myers (Taylor & Francis)
6.
Solid
State Electronics
(PH-506)
Network Theorems Thevenin's, Norton's, Millman's,
Compensation and Superposition Theorems, Decible notatations, Impedence
Matching.
Semiconductor Devices Shottky Diode, Tunnel Diode, UJT, LED, Liquid Cystal Diode and SCR. Operation of
an N-Channel JFET, Transfer and Output Characteristics of a JFET, Parameters of JFET, JFET as an Amplifier, Bising of
JFET, Principle and Operation of MOSFET in Depletion and Enhancement mode.
Operational Amplifier Difference Amplifier, Circuit details of Op-Amp 741, Inverting and Noninverting
Configurations, Measurement of Op-Amp parameters, Frequency Response of Op-Amp,
Op-Amp Applications- Mathematical Operations, Solution of Differential
Equations, High Resistance Voltmeter
Digital Electronics Boolean Algebra, Kranaugh Map, Karnaugh Simplifications, Don't Care Conditions,
Multivibrators- Astable and Monostable, Bistable, Schmidt Trigger, Flip Flops:
D, RS, JK, Master Slav JK, Register and Counters: Shift Register, Ripple
Counter, Up-Down Counter, Asynchronous and synchronous Counter, Ring Counter and
Sequence Generators, Memories: C-MOS, ROM, MOS, RAM, D/A and A/D Converters.
Wave Propagation Brief idea of Space Wave, Ground Wave and Sky Wave Propagation and Earth's
Ionosphere.
Modulation: Amplitude Modulation, Angular, Frequency and Phase Modulation, PPM,
PDM, PWM.
Radiation and Antenna (Brief idea), Transmitters and Receivers (Basics)
Books
1.
Operational Amplifier and other Application: Kumar & Sarkar
2.
Digital Principles and Application: Malvino Leach
3.
Integrated Electronics:
Milman & Halkias
4.
Operational Amplifier & Linear Integrated Circuit
Coughlin, Driscol
5.
Electronic Devices and Circuit Theory
Robert L. Boylestad, Louis Nashelsky
6.
Physics of Semiconductor Devices
M.Shur
7.
Electronic Principles
Malvino
M. Sc (Final)
1.
Advanced Quantum Mechanics (PH-601)
Scattering Theory:
Differential scattering cross
section, incoming and outgoing solutions, Expression for the scattering
amplitude, Born approximation and its validity, Green’s function, partial wave analysis, optical
theorem, relation between phases shift and potential, Ramsauer- Townsend effect,
scattering by a square well
potential, scattering by a hard sphere.
Relativistic Quantum Mechanics Relativistic Quantum Mechanics
The Dirac
Equation, Dirac Matrices, Solution of the free particle, Dirac Equation with
potentials, Equations of Continuity, Spin of the electron , Non realistic limit,
Dirac equation, for Hydrogen atom, spin orbit coupling, covariance of the Dirac
Equation , Bilinear covariants, hole theory, the Wele’sfor the neutrino, non conservatiThe principles of canonical quantization of fields, Lagrangian
density and Hamiltonian density, Second quantization of the Shrodinger wave
field for Bosons and fermions, quantization of the electromagnetic fields,
second quantization of the Dirac and Klien – Gardon fields,
Reference: fields, Lagrangian
density and Hamiltonian density, Second quantization of the Shrodinger wave
field for Bosons and fermions, quantization of the electromagnetic fields,
second quantization of the Dirac and Klien – Gardon fields,
2. pan style 3. Schiff- Quantum Mechanics
4. Sakurai- Advanc(PH-602)
Maxwell’s
equations and conservation lawseight:normal"
2.
Classical Electrodynamics MMaxwell’s
equations, vector and scalar potentials, Guage transformations, Lorentz gauge,
Coulomb gauge, Green functions for the wave equation, Poynting’s theorem and
conservation of energy and momentum for a system of charged particles and
electromagnetic fields, Transformation properties of electromagnetic fields and
sources under rotations, Spatial reflections and time reversal.
Plane
Electromagnetic Waves and Wave Propagation conservation of ene
Plane
waves in a nonconducting medium, Linear and circular polarization, Stokes’
parameters, Reflection and refraction of electromagnetic waves at a plane
interface between two dielectrics, Polarization by reflection, total internal
reflection, Goss-Hanchen effect, frequency dispersion characteristics of
Dielectrics, Conductors and plasmas, Waves in a conducting medium, Illustration
of the spreading of a pulse as it propagates in a dispersive medium, Kramers
Kronig relations.
Wave Guides and Resonant Cavities
Cylindrical cavities and wave
guides, Modes in a rectangular waveguide, Energy flow and Attenuation in
Waveguides, Resonant Cavities, Power losses in a cavity, Q of a cavity.
Radiating Systems, Multipole Fields
Fields and radiation of a
localized oscillating source, Electric dipole fields and radiation, magnetic
dipole and Electric Quadrupole fields.
Special Theory Of Relativity
Lorentz Transformations and
Basic Kinematic Results of Special Relativity, Addition of velocities;
4-velocity, Relativistic momentum and energy of a particle, vector and tensor
calculus, matrix representation of Lorentz transformations, Infinitesimal
generators, Thomas Precession, Invariance of Electric charge, Co-variance of
Electrodynamics, Transformation of Electromagnetic fields, Lagrangian and
Hamiltonian for a relativistic charged particle in external electromagnetic
fields, canonical and symmetric stress tensors conservation laws, solution of
the wave equation in
co-variant form, Invariant green
functions.
Radiation by Moving Charges
Lienard-Wiechert potentials
and fields for a point charge, Total power radiated by an accelerated charge:
Larmor’s formula and its relativistic generalization, Angular distribution of
radiation emitted by an accelerated charge, Thomson scattering of radiation,
Radiative reaction force from conservation of energy, Abraham- Lorentz
evaluation of the self force, Level Breadth and level shift of a radiating
oscillator, scattering and absorption of radiation by an oscillator.
Books:
Classical Electrodynamics – J.D.Jackson.
Emission of Alpha, Beta and Gamma rays.
Gamow theory of α-decay, Beta ray spectroscopy. Fermi theory of Beta decay.
Liquid drop model. Evidence of nuclear shell structure. Shell model: It’s
validity and limitations. Collective model.
Nuclear Forces and Nuclear Reactions
Nature of Nuclear forces. Elements of two–body problem. The Deuteron: Ground
and Exited state. Meson Theory of Nuclear forces. Spin dependence of nuclear
forces.Conservation laws. Various types of Nuclear Reactions. Nuclear Reaction
Kinematics. Q-value, Threshold energy. Compound nucleus. Direct reactions.
Stripping and pick-up reactions.
Nuclear Energy and Nuclear Reactors
Nuclear fission and fusion reactions. Mass and
energy distribution in fission fragments. Spontaneous fission. Bohr and
Wheeler’s theory of Nuclear fission. Neutron cycle in chain reactions. Four
factors formula. Components of nuclear fission reactors. Controlled
thermonuclear reactions. Theoretical aspects of nuclear fusion reactors.
Conditions of breakeven and ignition, confinement, pinch effect etc.
Elementary Particles
Classification and important properties of elementary particles.
Leptons, Baryons, Mesons and Hyperons. Particle and Antiparticle. Various types
of interactions existing in nature: Gravitational, Electromagnetic, Weak and
Strong interactions. Conservation Laws in fundamental interactions.
Excited state and resonance. Gellmann Nishijima formula. Quark Model. C.P.T.
invariance in different interactions. Parity non conservation in weak
interactions.
Books:
1. Segre: Nuclei and Particle
2. Cohen: Nuclear Physicse of Nuclear forces. Elements of two–body problem. The Deuteron: Ground and
Exited state. Meson Theory of Nuclear forces. Spin dependence of nuclear forces.
Conservation laws.
Various types of Nuclear Reactions. Nuclear Reaction
Kinematics. Q-value, Threshold energy. Compound nucleus. Direct reactions.
Stripping and pick-up reactions.
Nuclear Energy and Nuclear Reactors
Nuclear fission and fusion reactions. Mass and energy distribution in fission
fragments. Spontaneous fission. Bohr and Wheeler’s theory of Nuclear fission.
Neutron cycle in chain reactions. Four factors formula. Components of nuclear
fission reactors. Controlled thermonuclear reactions. Theoretical aspects of
nuclear fusion reactors. Conditions of breakeven and ignition, confinement,
pinch effect etc.
Elementary Particles
Classification and important properties of elementary particles.
Leptons, Baryons, Mesons and Hyperons. Particle and Antiparticle. Various types
of interactions existing in nature: Gravitational, Electromagnetic, Weak and
Strong interactions. Conservation Laws in fundamental interactions.
Excited state and resonance. Gellmann Nishijima formula. Quark Model. C.P.T.
invariance in different interactions. Parity non conservation in weak
interactions.
Books:
1. Segre: Nuclei and Particle
2. Cohen: Nuclear Physics
3. Enge: Nuclear Physics
4. Preston
and Bhaduri: Physics of Nucleus
5. Elton: Introductory Nuclear Theory
6. Bethe: Nuclear Physics
7. Blatt and Weiscopff: Nuclear Physics
8. Kaplan: Nuclear Physics
9. W.E.Burcham and M.Jobes: Nuclear and Particle Physics
4.
Nanophysics & Technology (PH-604)
Introduction
Review of Nanotechnology, Ideas about building things with atom, Possible
applications in science & Technology.
NanoPhysics Physics of
low dimension system: Length scale, Quantum confinement, Particle in a 1D, 2D
spherical box, Particle in a circle, Density of states of quantum well, quantum
wire and quantum dot.
Techniques used in Nanotechnology
X-ray crystallography, Particle size determination, Surface
structures. Microscopy: TEM, SEM, STM & AFM, Nuclear Magnetic Resonance, Chzochralski technique,
CVD, Oxidation Diffusion ion implantation, Photolithography, Etching,
Metalization.
(a) Properties of Individual Nanoparticles. Metals nanoclusters, Semiconducting nanoparticles.
(b) Bulk Nanostructured Material:
Solid disordered nanostructures: Method of synthesis, Failure mechanism of
conventional rain-size
materials, mechanical properties, Nanostructured
multilayers, Electrical properties, Metals nanocluster composite glass,
Porous silicon.
(c) Quantum wells, Wires and Quantum Dots
Nanotechnology in Carbon Materials
Fullerenes and Carbon Nanotubes, Fullerene as nano structures of C-C
and higher fullerene, Electronic properties of fullerene and carbon tubes as
Nano-structures, Structure of carbon Nano tubes, Electronic structure of C-Nano
tubes
Books
1. Introduction to Nanotechnology by C.P. Poole, Wile, Interscience (2003)
2. Nano-Technology by Gregrory Timp (Editor) AIP Press Springer (1998)
3. Carbon nanotubes Synthesis structure, Properties and Applications by M.S.
Dresselhaus, G. Dresselhaus Avouris
(Springer Berlin 2001)
5. Material Science (PH-605)
Experimental methods for
Crystal
Growth Growth for melt:
Bridgman -Stockbarger and Czocharalski method , zone melting technique. Growth
by vapour : Sputtering technique
Growth from liquid solution : Hydro thermal method
Atomic Imperfections in Crystals Point imperfections in crystals: substitutional,
impurity, vacancy, interstitial etc.Line imperfections: Edge and screw
dislocation, Burger vector and Burger circuit, dislocation motion, energy of
dislocation, dislocation multiplication, slip planes and slip directions,
perfect and imperferct dislocation reaction Surface imperfections: Tilt and
twist boundry, Stacking faults
Color centers
Atomic diffusion in crystals
Mechanism of diffusion, Fick's second law, steady state solution-
diffusion through a plane surface, diffusion through a cylinder , diffusion
through a sphere; non steady-state solution, some applications of diffusion-
experimental determination of diffusion coefficient , corrosion resistance of
duralumin, decarburization of steel; doping in semiconductors , the Kirkendall
effect, the atomic model of diffusion , diffusion in alkali halides , ionic
conductivity in alkali halide crystals , diffusion and ionic conductivity.
Atomic Packing in Crystals Close packing of spheres, Axial ratio and lattice constants,
Voids in close -packing, cordination of voids, Rules governing the packing of
atoms, Effect of radius ratio, Application of Pauling rules to actual
structures, Representation of closest packing, polymorphic and polytypic
structures, Polytypic notations, stacking faults in fcc, hcp crystals.
Phase Diagrams
Definition, explanation of Phases, phase diagram of pure substances (
water, and iron ) Gibb's phase rule, Binary amorphous alloy systems, the Lever
rule, Binary eutectic alloy systems , binary peritectic alloy systems, binary
monotectic systems, invariant reactions, their representations and examples.
Characterization Techniques Principles, analysis and applications of (i)
I.R spectroscopy (ii) Spin resonance spectroscopy (iii) Transmission
electron microscopy (TEM) (iv) Scanning electron microscopy (SEM) (v) X-ray
photo electron spectroscopy (vi) Auger electron spectroscopy (AES) (vii) Raman
spectroscopy
Miscellaneous Materials Amorphous materials , Polymers, Semiconductors -III-V and
II - VI compounds, Giant magneto resistance (GMR) materials, colossal magneto
resistance (CMR) materials, piezo electric and ferroelectric materials.
Books:
1. Solid
State
Physics -
M.A. Wahab
2. Amorphous Mterials -
S.R.
Elliot
3. Material Science
-
W.F. Smith
6 .Advanced
Solid
State Physics (PH-606)
Lattice Dynamics
General theory of lattice dynamics,
Normal co-ordinate description, Quantization of lattice vibrations, Phonon
concept, Inelastic scattering of slow neutrons by crystals for study of phonons,
Calculations of phonons in different types of crystals.
Electronic energy band
Calculations of energy bands and Fermi surfaces and other related
properties like density of states, Tight binding method, Cellular method, Muffin
tin potentials, Augmented plane wave method (APW), Green's functions (KKR)
method, Orthogonalized plane wave (OPW) method, Correlation.
Optical Properties
Phonon-Phonon interaction, Kramers-Kronig relations, Polarizability
and dielectric constant of ionic crystals, Raman scattering by crystals,
Interaction of Electromagnetic radiation of with solids, Dielectric function,
Absorption of Electromagnetic radiation, Dielectric function for a harmonic
oscillator, longitudinal and transverse normal mode, surface waves on a
dielectric, Reflectivity of a dielectric half space, Interband transition,
Excitons, Dielectric energy losses of electrons.
Excitations in imperfect crystals
Elementary ideas of Green's function method for a vibrational spectrum for point
defects in imperfect crystals, ionized gap modes and resonance modes.
Many electrons system
Fermion fields, Hartree and Hartree-Fock approximation, self
-consistent field method, Dielectric relation analysis, Dielectric screening
random phase approximation, Dielectric constant of electron gas, Dielectric
screening of a point charge impurity.
BOOKS 1.
J.M. Ziman: Princiles of Solid
State Physics
2. M. Born and K. Huang: Theory of Lattice Dynamics
3.
G. Venkatraman: Dynamics of
perfect Crystals
4. Band Structure
Theory: J. Callaway 5. Lattice Dynamics Vol. II:
Academic Press
2. B. Tech
(i) Physics-I (PH-101)
(Credit-4)
Free Oscillations
Free oscillations in one dimension (Mass- Spring,LC circuit) longitudinal and
transverse oscillations, Superposition principle, Beats ,Transverse modes of
continuous string, classical wave equation, standing waves , wave velocity,
Fourier analysis of a function, Fourier coefficient,
Normal
modes, Dispersion relation.
Forced Oscillations
Damped harmonic oscillation, steady
state oscillation under periodic force, Resonance, various cases of
resonance-Mechanical and electrical low pass filters.
Progressive Waves One dimensional harmonic
traveling waves, dispersive & nondispersive waves, phase velocity, index of
refraction, characteristic impedance, energy transport by traveling wave,
reflection and transmission, Impedance matching between two transparent media,
Modulation of pulses & wave packets, group velocity, Fourier analysis, Coupled
oscillations.
Interference & Diffraction
Interference between two point
sources, constructive and destructive interference, Young’s double slit
experiment, interference at far points, relative phase coherence condition,
Newton’s rings; Lloyds single mirror, single slit diffraction,
angular width of diffraction limited beam, angular resolution of human eye,
Fraunhofer &Fresnal diffraction. Two slits & many slits diffraction pattern,
Angular width of principal maxima.
Polarization
Description of polarization states,
production of polarized transverse waves, Double refraction.
Some Special Topics
(a)
Structure
of crystalline solids, free electron model. Failure of this model, Periodic
potential, Band theory. Fermi energy, metals insulators & semiconductors.
(b)
Wave
mechanics, Schrödinger’s equation. Time independent Schrödinger’s equation,
Particle in a box, step potential, Tunneling phenomena.
Books
Waves and oscillation:
Berkeley physics course III,
Fundamental of optics: Jenkins and White ,
Introduction of solid state physics: C.Kittel ,
Solid State physics: A.J.Dekker,
Quantum Mechanics: Powell,
Quantum Mechanics: Singh and Bagdel,
Quantum Mechanics: Schiff
(ii) Physics-II (PH-102)
(Credit-4)
Electrostatics
Coulomb’s law, Electric field, field
due to continuous charge distribution, a
line of charge, sheet of charge etc., Electrostatics potential, Potential
of a charge distribution, Gradient of potential, Dipole, Field due to a dipole(general), Torque, Energy.
Gauss’s law and its applications, Capacitors, energy stored in capacitors.
Dielectrics
Energy of an electric field,
Polarization, Dielectric constant, Susceptibility and Permittivity, Field in dielectrics,
Atomic Theory, Polarizability, Cassius-Mosotti relation.
Electric Current
Electric current, Current density, Ohm’s law,e.m.f.,
RC circuits.
Magnetic Field
Magnetic field and currents, Ampere’s law,
Biot-Savart’s law, Motion of Charge in electric and Magnetic field, cyclotron,
mass spectrograph, divergence & curl of fields. Magnetic vector potential,
Magnetic dipoles, torque & energy, dipole moment, electron in an orbit.
Magnetic field in matter
Magnetization, the three magnetic
vectors (B,M&H) units, susceptibility and permeability, Dia, Para, and
Ferromagnetism, Magnetic domains, Hysteresis, Maxwell’s equations in free space
and in matter, Ferroelectrics.
Electromagnetic induction
Magnetic flux, Faraday’s law, Lenz’s
Law, Motor & generators, Time varying magnetic field, Betatron self and mutual
inductance, RC, LR and LCR circuit,
Energy density in magnetic fields
Maxwell’s Equations
LC oscillations, Displacement Current, Maxwell’s
equation in vacuum & matter (Integral and Differential form’s), conservation of
electromagnetic energy, Poynting theorem, Radiation from a point charge.
Electromagnetic wave
Wave equation, Plane waves, wave through
non-conducting medium, Polarization, reflection and transmission, Snell’s law.
Books:
1.
Electricity and Magnetism:
Berkley Physics Course II.
2.
Electromagnetic waves & Radiating systems: Jordan and Keith.